SOLUTION: Raj, Ismail and Carol went shopping. Raj spent 0.25 of the total amount that Ismail and Carol spent. Carol spent 4/11 of the total amount that Raj and Ismail spent. Ismail spent $3

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Raj, Ismail and Carol went shopping. Raj spent 0.25 of the total amount that Ismail and Carol spent. Carol spent 4/11 of the total amount that Raj and Ismail spent. Ismail spent $3      Log On


   

Question 1203261: Raj, Ismail and Carol went shopping. Raj spent 0.25 of the total amount that Ismail and Carol spent. Carol spent 4/11 of the total amount that Raj and Ismail spent. Ismail spent $37.50 more than Raj. If Ismail had $90 before he went shopping, what fraction of his money did he spend? (Answer in Simplest form)
Found 2 solutions by greenestamps, MathTherapy:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Raj spent 1/4 as much as Carol and Ismael together, so the fraction of the total that Raj spent was %281%2F4%29%2F%281%2B%281%2F4%29%29=%281%2F4%29%2F%285%2F4%29=1%2F5

Carol spent 4/11 as much as Raj and Ismael together, so the fraction of the total that Carol spent was %284%2F11%29%2F%281%2B%284%2F11%29%29=%284%2F11%29%2F%2815%2F11%29=4%2F15

So of the total that was spent, the fraction that Raj and Carol together spent was 1%2F5%2B4%2F15=3%2F15%2B4%2F15=7%2F15

That means the fraction of the total that Ismael spent was 1-7%2F15=8%2F15

The amount Ismael spent was $37.50 more than the amount Raj spent:

%288%2F15%29x-%283%2F15%29x=37.50
%285%2F15%29x=37.50
%281%2F3%29x=37.50
x=112.50

The total the three of them spent was $112.50.

The amount Ismael spent was 8/15 of the total: %288%2F15%29%2837.50%29=8%287.50%29=60

Ismael spent $60.

He started with $90, so the fraction of his money that he spent was 60/90 = 2/3.

ANSWER: 2/3

Answer by MathTherapy(10549) About Me  (Show Source):
You can put this solution on YOUR website!
Raj, Ismail and Carol went shopping. Raj spent 0.25 of the total amount that Ismail and Carol spent. Carol spent 4/11 of the total amount that Raj and Ismail spent. Ismail spent $37.50 more than Raj. If Ismail had $90 before he went shopping, what fraction of his money did he spend? (Answer in Simplest form)

Let amount Raj, Ismail, and Carol spent be R, I, and C, respectively
Then we get: R = .25(I + C)_____R = .25C + .25I ----- eq (i)

                                                   
                                                   matrix%281%2C6%2C+4R%2C+%22=%22%2C+11C+-+4I%2C+%22-----%22%2C+eq%2C+%22%28ii%29%22%29 

                                                     I = R + 37.5
                                                     R = I - 37.5 --- eq (iii)
                                                    4R = C + I ------ Multiplying eq (i) by 4 ---------- eq (iv)
                                                     0 = 10C - 5I --- Subtracting eq (iv) from (ii) ---- eq (v)
                                                matrix%281%2C3%2C+-+10C%2C+%22=%22%2C+-+5I%29
                                                    

                                                   44R = 11C + 11I ---- Multiplying eq (iv) by 11 ---- eq (vii)
                                                   40R = 15I ---- Subtracting eq (ii) from eq (vii)
                                                 5(8R) = 5(3I)
                                                    8R = 3I ---- eq (viii)
                                           8(I - 37.5) = 3I ------- Substituting I - 37.5 for R in eq (viii)
                                              8I - 300 = 3I
                                                 - 300 = 3I - 8I
                                                 - 300 = - 5I 
                            Amount Ismail spent, or matrix%281%2C5%2C+I%2C+%22=%22%2C+%28-+300%29%2F%28-+5%29%2C+%22=%22%2C+%22%2460%22%29

Since Ismail had $90, initially, and spent $60, he spent