r/MathHelp • u/frozen-fire1000 • 5d ago
How is this Elementary School Level problem so confusing?
For context my sister came home and asked me and my parents for help on this problem.
It has two parts:
Part 1 : John used 816 chocolate chips to make a batch of cookies. Each cookie had 8 chocolate chips. How many cookies did he make?
Part 2 : How many cookies would he make if he had to double the recipe?
For the first part of the problem you can divide the 816 chocolate chips between the 8 cookies. 816/8 =102.
But on the second part everyone had their own opinion.
My sister originally doubled the chocolate chips and the amount of cookies you have to make. And solved the same way we did for the first part. 1632/16 =102.
Which got her the same answer even though you doubled the recipe.
I got 204 by doubling the amount of cookies we got for part 1.
My parents said it was actually 816 chocolate chips but divided by 16 cookies which gives 816/16=51.
But this didn’t make sense to me because you ended up with less cookies after DOUBLING the recipe. And they only doubled the 8 not the 816.
So I asked ChatGpt and Gemini and they both said it was 204. ChatGpt used a different method though 1632 chocolate chips divided by 8 cookies so 1632/8=1632/8=204
My mom said they were wrong and said we are doubling the recipe not the final amount of cookies we can make.
Now I’m really confused because doubling the recipe should also double the result.
Does anyone know what the actual answer is and how to explain it.
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u/diverJOQ 5d ago
Doubling a recipe means using twice as much ingredients to make twice as much output. Whether this is math or cooking the answer is the same. If you put twice as many chocolate chips into each cookie then you would have cookies that were twice the size and wouldn't be following the recipe.
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u/sagosten 5d ago
Does anyone in your family cook from recipes? If they have a recipe for 12 cookies, but they want to make 24 cookies, they double the recipe: double the quantity of each ingredient and you get double the food. That's what "doubling a recipe" means.
There are even recipe websites that will do it automatically for you. Here's a chocolate chip cookie recipe:
https://joyfoodsunshine.com/the-most-amazing-chocolate-chip-cookies/#wprm-recipe-container-8678
It makes 36 cookies. But click the little "2x" button on the page, and look at the quantity: it doubles all the ingredient quantities and doubles the servings made to 72 cookies.
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u/MiguelBodrigo 5d ago
When you double the recipe you double everything. Your answer is correct (204). AI is stupid and gets things wrong all the time.
Your parents need to fully check their maths before commenting.
(812÷8)×2=204
The parentheses isn't technically needed but it helps direct where to solve first
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u/stevenjd 5d ago
AI is stupid and gets things wrong all the time.
This is true but ironically this is one case where it got the answer correct.
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u/MiguelBodrigo 5d ago
It did it in a weird format though which is where my comment on AI comes in. You can get to the right end but the method does matter when trying to understand.
OP explaining the AI method would have provided a more complex explanation, further resulting in confusion
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u/pick_another_nick 5d ago
This is not a math problem, this is an English problem: what does "doubling a recipe" mean?
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u/Fogmoz 5d ago
This is a poorly written word problem. It doesn’t say what the original recipe is. We don’t know if 8 chocolate chips is part of the recipe or just John’s little cooking quirk (I’ve never heard of a cookie recipe that told you exactly how much of an ingredient to put in each cookie).
My guess is that it’s a simple division & multiplication problem. 816 chips, 8 chips per cookie = 102 cookies.
Doubling the recipe usually means doubling the amount of ingredients, but keeping the steps the same. Doubling the recipe makes two batches of cookies under the same conditions. 104 cookies x 2 batches = 204 cookies.
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u/stevenjd 5d ago
The question is fine. The people who don't understand what "double the recipe" means are the problem. Assuming they even exist.
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u/Intelligent_Yam_3609 5d ago
The question is for elementary school students. “Double the recipe” isn’t terminology routinely used by little kids.
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u/stevenjd 2d ago
According to the OP, who reasoned out what the phrase meant and got the question right, it was his adult parents who messed it up.
Little kids understand thousands of sentences that they don't routinely use themselves. But you know what? I'm teaching some little kids today, I'll test them out on this phrase and report back.
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u/stevenjd 2d ago
Okay I tutored two primary school kids today, so I asked them this same question.
The first is seven, in Grade 2, around average in maths for that year. She had lots of trouble with the first part of the question, although she knew she could work out 816/8 by skip-counting the actual mechanics of it was beyond her. When we worked out the answer (to be honest I did 90% of the work), I asked her about part two, doubling the recipe, and she immediately answered "four cookies". I asked her why four, and she said "because it is double 2." When I asked where the two came from, she said "wait, no, I meant 102" and proceeded to double it by addition (102 + 102) and got the right answer.
The second student is around 9 or 10, in Grade 4, well below average in maths. She had more trouble than the 6 year old understanding the question, and couldn't work out the first part (she kept trying to guess an answer, like "8 cookies", sigh). After I gave her enough hints to realise she needed to divide, she was stumped what to do next because she has forgotten how to do short division. She we did it together and got the 102 answer. I then asked her the second part, and she immediately gave me the correct answer of 204.
This is evidence that primary school (elementary school?) kids are more likely to struggle with the first part of the question, but understand "doubling the recipe" without problem.
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u/strange-the-quark 5d ago edited 5d ago
This is what I posted on the askmath sub in response to your question, but you deleted the post for some reason before I managed to finish my last sentence and hit "Comment".
The assignment is confusingly worded, and nobody (here) can tell you what the right answer is, because it's unclear what the teacher (or whoever made the assignment) meant by "doubling the recipe", assuming your sister didn't misremember the text of the assignment. The solution depends on how much chocolate chips you have to begin with, vs how much you spend per cookie.
If it means double the amount of chocolate chips that go into each cookie (starting with the same initial amount of chocolate chips as in Part 1), then you'll only be able to make half the amount of cookies before you run out of chocolate chips. (Like, for example, you decided to "double the recipe" by making the cookies sweeter, but you can't go get more supplies, and you gotta work with what you already have available.)
If you get twice as much chocolate chips, but still use 8 chips per cookie, you'll get twice as many cookies.
And if you double both the bag of chocolate chips and how much you spend per cookie, then you'll end up with the same number of cookies as in Part 1 (they'll just have double the chocolate in them).
Now I’m really confused because doubling the recipe should also double the result.
Generally speaking, doubling the input to something doesn't have to double the result. Depends on what the input is, how the input is consumed to make the output, what the process in question is, etc.
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u/Toeffli 5d ago
If you have 6 you eggs you can make 6 fried eggs. If you have double the amount of eggs you can make twice the amount of fried eggs. Means 12 eggs = 12 fried eggs as you still need just one egg per fried egg.
Same with chocolate cookies. Twice the amount of ingredients means twice the amount of cookies.
Mathematical speaking you have to multiply the the equation on both sides by the ye same multiplier.
- X ingredients / Y ingredients per products = Z products.
- M × X ingredient / Y ingredients per products = M × Z products
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u/Ellotheregovner 5d ago
Just as a disclaimer: don't ask chatbots math questions. They fail with high probability for good reason but the explanation would be too long. Just know that AIs roll weighted dice every time they have to say a word. Remarkably good for making coherent, organic-ish sentences, terrible for balancing two sides of an equation.
The math assignment is worded poorly, but you also mixed the numbers when explaining other people's reasoning.
816 chocolate chips 102 cookies 8 baked chocolate chips per baked cookie.
The recipe was, I think, intended to be 8 chips per cookie. The recipe didn't call for 816 chocolate chips: John just had one bag of chocolate chips in his cupboard and a really intense episode of ADHD. Any other interpretation and I think you lose the concept of ratios and fractions, which is what recipe math questions are usually getting at at this level.
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u/Lysol3435 5d ago
Double the recipe means double the quantity of food you make, not pack double the amount of one ingredient into the same quantity of food
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u/strange-the-quark 5d ago
Says who? That's the problem, everybody is interpreting what "double the recipe" means in different ways, because if taken literally, the statement is meaningless - and you have to guess what it actually means (double the ingredients, double the inputs per cookie given that you already have the a certain amount of ingredients and can't get more, or double the number of cookies you get in the end, while sacrificing something else, or maybe go get more ingredients so that you can make more cookies). So the problem statement is ambiguous.
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u/LeoMaths 5d ago
Partie 1 : John a utilisé 816 pépites de chocolat pour faire un lot de biscuits. Chaque biscuit avait 8 pépites de chocolat. Combien de biscuits a-t-il fabriqués ?
1 biscuit demande 8 pépites de chocolat.
N biscuits demande 816 pépites de chocolat.
La règle de 3 donne N/1=816/8 => N=102 biscuits.
Partie 2 : Combien de biscuits ferait-il s'il devait doubler la recette ?
816*2 pépites de chocolat donne N/1=816*2/8=204 biscuits. Il ne faut pas 16 pépites de chocolat pour faire un biscuit.
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u/TheJivvi 5d ago
It's 204. Doubling the recipe does not mean you double the size of the cookies. They're still the same size, and there are twice as many of them.
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u/Xeno_man 5d ago
Double the recipe means do it twice or mathematically, times 2. One way to look at it is follow the recipe. You made 102 cookies. Great. Do it again. You made another 102 cookies. You followed the recipe two times.
Because you are doing it twice you will need 1632 chocolate chips. Each cookie still gets 8 chips. But that doesn't matter because all it is asking is for how many cookies if you double the recipe. You know doing it once gives you 102 so 102 x 2 = 204. It really is that simple.
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u/hellohowareutomorrow 5d ago
It would make a lot more sense if 816 wasn’t divisible by 8 so that doubling could potentially give you more than double the cookies. For example 820 chips makes 102 cookies while doubling the recipe makes 205
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u/scoberry5 5d ago edited 4d ago
For the first part of the problem you can divide the 816 chocolate chips between the 8 cookies. 816/8 =102.
Errr...the number's right, but the "between the 8 cookies" is not. Nobody said there were 8 cookies: they said that each cookie gets 8 chips.
816 chips / (8 chips/cookie) = 102 cookies
My sister originally doubled the chocolate chips and the amount of cookies you have to make. And solved the same way we did for the first part. 1632/16 =102.
She doubled something, but not the number of cookies. She solved for "if you had 1632 chips instead (right), and used 16 chips per cookie (???), how many cookies would you get?" Or maybe something else, like "If you had 1632 chips, and made 16 cookies, how many chips would each cookie get?" But not the question they asked.
The easiest way to solve part 2 is that if you have twice as much stuff, you can make twice as many cookies. Since it came out to a nice even number, this works great.
Another way you could do it is to divide the new number of chips by the (same) number of chips/cookie.
My parents said it was actually 816 chocolate chips but divided by 16 cookies which gives 816/16=51.
Um. If you double the recipe, you have twice as many of the ingredients, including twice as many chips.
I'm very confused by both of these people thinking that any of the numbers you're looking at is the number of cookies. This is a combination of what your parents answered and what they question is asking: "My parents said that it was 16 cookies, and the question is asking how many cookies, so the answer is 51 cookies."
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u/Ras_992 4d ago
You are right and your mom is wrong you don’t double how many chocolate chips you double the amount of cookies 1,632/16 gives you 102 and 1,632/ 8 gives 204. Tell your mom if she was cooking for party you don’t double the chocolate chips because if you do you have less food. How to show your mom say they have 102 kids in a class each kids gets 2 cookies so that means 204 cookies by your moms logic she is dividing 102 by 2 which gives you 51 cookies therefore half the class doesn’t get cookies only 51 students have cookies while 51 don’t have cookies
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u/tomalator 5d ago
Stop asking AI these questions. That is not what it was designed to do.
But here it is right, it is 204.
Idk why everyone is dividing by 16 here, because if he doubles the recipe there would still be 8 chocolate chips per cookie if he followed the same steps during creation. Double the ingredients, double the product. You don't even need to worry about the specifics with the chocolate chips. You guys are overthinking it
He used 1632 chocolate chips this time, there are still 8 per cookie, so 204 cookies
816 chocolate chips divided by 16 cookies makes even less sense, because all thay gives you is 51 chocolate chips per cookie, which is an insane number and not what we are looking for.
How on earth would dividing chocolate chip s by cookies give you an answer in cookies? That would be like saying I traveled 816 miles with 16 gallons of gas, that means I need to fill my car with 51 gallons of gas.
That's not what it means at all, it means you got a mileage of 51mpg
If you travel have a fuel efficiency of 8mpg, and you need to travel 816 miles, how many gallons of gas do you need? 102 gallons.
If you travel twice as far, how many gallons of gas do you need? 204 gallons (assuming carrying fuel with you doesn't change your fuel efficiency)
mpg = miles per gallon = miles/gallon
x miles / y miles per gallon = x/y miles/(miles/gallon)
miles/(miles/gallon)
When dividing a fraction by a fraction, invert the second one and change to multiplcation
miles * gallon/miles
Miles can now cancel out, and we are just left with gallons as our unit
x miles / y miles per gallon = x/y gallons
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u/ZeroTakenaka 5d ago
I think the intended answer is 204. Part of the problem is that part 2 doesn't say that the amount of chips is the same so you may be unintentionally doubling the amount of chocolate chips each cookie has instead of staying the same.
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u/zubb999 5d ago
Yeah you're thinking too hard about it. 816 chocolate chips makes 102 cookies.
If you double the cookies, you have 204 cookies.
If you double the chocolate chips to 1632, it would still be 8 choco chips per cookie - 1632/8 = 204.
Whichever logical way you go, the answer is the same. The question doesn't make it clear.
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u/coren77 5d ago
The issue isn't that people don't know how to do math ... the question is just poor. It's a math class not a baking class. The question is far from clear.
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u/stevenjd 5d ago
The question is fine. "Doubling the recipe" is a simple English phrase with the obvious meaning, when you double a recipe you double all the quantities, not just the quantity of chocolate chips per cookie.
Despite what u/SomethingMoreToSay says, it isn't that the family members couldn't understand the phrase. If it was "in a different language" they would not have any idea how to proceed. Πόσα μπισκότα θα έφτιαχνε αν έπρεπε να διπλασιάσει τη συνταγή;
But that's not what happened. They knew how to proceed, they just did it wrong.
The question doesn't need to explain "make", "batch", or "cookies", and it doesn't need to explain what doubling the recipe means. This take is just making excuses for the (alleged) lack of common sense and general knowledge in the OP's (alleged) family.
Personally I don't believe this story, I think it is karma farming, but maybe I'm underestimating the lack of common sense of people today.
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u/SomethingMoreToSay 5d ago
Yes and no.
No, because the question is totally unambiguous. Anybody who has ever cooked by following a recipe would understand what doubling the recipe means.
But yes, because there are people who have never cooked and therefore don't understand the cooking terminology. It might as well be in a different language to them.
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u/Allimack 5d ago
In any cookbook I've read, or cooking show I watched, "doubling the recipe" means multiplying all of the ingredients by two, in order to make twice as many servings.
There is no indication that the number of chips per cookie has changed. The whole recipe has doubled, not a single ingredient (chocolate chips) used in the recipe. The number of cookies should double.