SOLUTION: Hi Alex had $57 less than Belle. Alex saved 3/5 of his money while Belle spent 2/3 of her money. Given that the amount Alex spent was 1/4 of Belles savings how much did Belle spen

Algebra ->  Finance -> SOLUTION: Hi Alex had $57 less than Belle. Alex saved 3/5 of his money while Belle spent 2/3 of her money. Given that the amount Alex spent was 1/4 of Belles savings how much did Belle spen      Log On


   

Question 1205347: Hi
Alex had $57 less than Belle. Alex saved 3/5 of his money while Belle spent 2/3 of her money. Given that the amount Alex spent was 1/4 of Belles savings how much did Belle spend
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
let the amount of money Belle has be x
if Alex had $57 less than Belle, he has x-57
if Alex saved 3%2F5+of his money , he saved %283%2F5%29%28x-57%29=> so, he spent %282%2F5%29%28x-57%29
if Belle spent 2%2F3 of her money, she spent %282%2F3%29x=>Belle’s savings is %281%2F3%29x
Given that the amount Alex spent was 1%2F4 of Belles savings how much did Belle spend
%282%2F5%29%28x-57%29=%281%2F4%29%281%2F3%29x
%282x%29%2F5+-+114%2F5+=+x%2F12
%282x%29%2F5+-x%2F12++=114%2F5+
%2819x%29%2F60++=114%2F5+
19x++=60%28114%2F5%29+
19x++=1368
x++=1368%2F19
x++=72

how much did Belle spend
answer: she spent : %282%2F3%29%2A72=48

check:
Belle had $72=> she spent 2%2F3 of her money $%282%2F3%2972=48 and saved $72-48=24
Alex had $72-57=15=> he spent 1%2F4 of Belles savings which $%281%2F4%2924=6 and saved $15-6=9

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Tutor @MathLover1 showed a typical formal algebraic solution starting from one obvious starting point: the amounts Alex and Belle had in dollars were x and 57-x. The solution is obtained with standard algebraic processes from there that involve moderately awkward calculations.

One important lesson to learn when beginning the study of algebra is that most problems can be set up in many different ways, leading to solutions involving calculations that are of very different levels of difficulty. It is a good idea to consider different possible ways of setting up a problem to try to find one that makes the actual calculations as easy as possible.

After playing a bit with the given fractions, here is the method that I came up with that is probably about the easiest for solving the problem.

Alex saved 3/5 of his money, so...

Let 3x = amount Alex saved
Let 2x = amount Alex spent

Then 8x = amount Belle saved (the amount Alex spent was 1/4 of what Belle saved)

Then 16x = amount Belle spent (Belle spent 2/3 of her money, so the 8x she saved was 1/3 of her money; that makes the 2/3 of her money that she spent 2*8x = 16x)

The amount Alex had was $57 less than the amount Belle had:

3x%2B2x=%288x%2B16x%29-57
5x=24x-57
19x=57
x=3

ANSWER: The amount Belle spent was 16x = $48