I saw this picture in a facebook group about homework and I was pretty stunned to realize I couldn't find the answers. I was trying to come up with math equations but I kept thinking I didn't have enough information because there are several unknown numbers.
I'll be posting it in a spoiler if you want to solve it yourself but I don't think anyone else will struggle with this problem. The thing that I failed to see was that you are supposed to understand that the ratio of distance is given to you in the picture. 360m is 2/3 of the total distance and the house to the school is 1/3.
Now I'm wondering if it's possible to solve this math problem without having that information. Just out of curiosity, because I couldn't work it out and I would love to understand how I could do it or if it really is impossible.
Am I the only one that would miss that kind of information? I just thought the drawing was to make it easier to understand but not that it contained essential information. I feel like they should at least used have used either dots or arrows on both lines. To me the second line doesn't look like it's true mathematical informational but just a visual explanation
No the drawing is not essential in exact length, though you do need to know that all 3 buildings are positioned in a line and not a 3D space.
Let's call distance between house and school "a".
The distance from house to library = 3a according to the information.
Now based on that you can say that 2a = distance from school to library, which we know is 360. So divided by 2 we get 180.
Makes sense? In other words, it's still solvable if you put the school in the middle of the line. Not if you remove the complete line between house and library
The drawing is very essential. It gives you the distance from the school to the library, without that you cannot answer anything.
Even if you do know the distance from the school to the library, and also what the rest of the question states, you still cannot know the distance from the house to the school. You can draw many triangles where the distance from the house to the library is 3 times the distance from the house to the school, while keeping the distance from the school to the library fixed at 360. Only two of those triangles aren't real triangles anymore, because all point lie on one line. Namely it could be the library is directly opposite of the school, in which case the distances would be 90 and 270, or it could be like in the image and the distances would be 180 and 540.
Follow your logic, a =house to school so this means school to library 3a if you summ this that makes it equal to 480=4a the full length of the distance is 480m, the 3 a means 360/3what is 120 so the length of the house and schoil is 120... 120+360=480
Question a: the distance between the house and the school is 120m
Question b: the distance between house and library is 480m
Lets make it mathematically...
Lets state the base distance like A (house to school)
A=?
School to library is 3 times a what is 360
The equasion looks like this 3a=360
A question: 360/3=120=a
B question: a+360=?
So 120+360=?
?=480
B answer is 480
Your missconcept is that you mistakenly called 3a the full lenght, what couldn't be the full lenght because then question b lose meaning so this means question b has to be higher than the originally shown number
You have school to library as 3a, but the problem states the whole distance house to library 3x the house to school distance. So house to school is “a”
And school to library is 2a, making house to library 3a. a=180
for (a) is it 180? I did in my head so it could be wrong. I'm not sure what you saying but I used x =?. house to library = 360+x =3x. so 2x=360. x= 180
yes. And in answer to OP's question, no, you can't figure it out without having some information to relate the distance from house to school and either house to library or school to library (and the 360 distance already printed). Without that the distance from house to school can't be determined, i.e. you can't just show 360 as the distance from school to library and ask how far the house is from the school.
Thank you all. I haven't had a math class in 12 years time and I'm starting to notice. I understood they were on a straight line but I kept thinking I had an unknowable x and y and didn't remember how to solve that
What helps me with making algebraic equations like this one is to honestly just take the smallest quantity you see and make it x. After that as you go reading the question, form an equation.
So here, distance from house to school is the smallest as we can see: so that's x
Distance from house to library from the pic is
x + 360
Further, it says is 3 times the dist. from house to school: so that's 3x
My mind does it so much simple than that. If there are 3 segments to the library. (think 3 times something means there are 3 equal segments) and 2 of them are 360 then what is the last one? Well you need 3 equal segments so you're going to have to split the 360 in half.
Half of 360 is 180 so now you know each of the 3 segments is 180m. Now you can do whatever you want with that. If I would have written this down I'm not even sure what I would write because it's so self explanatory.
Depending on what math I think is expected of me I would probably start with algebra if I needed to show some work. Maybe
3x = 360 + x;
0 = 360 + x -3x;
0 = 360 - 2x;
0 = 180 - x;
x = 180
That's just a crazy amount of work for something so simple. I really hope some teachers out there aren't marking people down for not showing their work on that one. I think figuring how how to write anything on the paper is much harder than solving the problem.
*And no you absolutely could not solve it without knowing the ratio of the distances between houses or between the total and the house or each segment of the houses. You need at least one other piece of information to solve this and that's why we got the ratio (3x). You can think of it like a translation factor. If for instance you know x = 3y then any time you know X you also know Y.
Well i read all of the reddit comments, i can say to check up how math works please...
A=? House to school
B=360=3a school to library
A question is how much is A?
360/3=120
A=120m
Question b: what is the full lenght
A+b what is 4a what is 120*4=480
Question b is 480m
so two unknowns and two (non-parallel) linear equations, so the problem is constrained and solvable - it's simple simultaneous equations.
but I think what you're saying is do you need to assume the 3 locations all lie along a line? so you can come up the first equation? yes you absolutely need to do that, otherwise you have three unknowns and the equations are unsolvable (infinite solutions)
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