SOLUTION: David spent $75 of his money on some t-shirts. He spent 1/4 of the remaining money on some batteries. Given that he was left with 1/3 of his original sum of money left, how much mo

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: David spent $75 of his money on some t-shirts. He spent 1/4 of the remaining money on some batteries. Given that he was left with 1/3 of his original sum of money left, how much mo      Log On


   

Question 1202333: David spent $75 of his money on some t-shirts. He spent 1/4 of the remaining money on some batteries. Given that he was left with 1/3 of his original sum of money left, how much money did David have at first?
Found 4 solutions by math_tutor2020, mananth, ikleyn, MathTherapy:
Answer by math_tutor2020(3817) About Me  (Show Source):
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Answer: $135


Work Shown:

x = starting amount of money
x-75 = amount left after buying the shirts
(1/4)*(x-75) = amount spent on batteries
(3/4)(x-75) = amount leftover after buying the batteries

Note that 1/4 + 3/4 = 1 = 100% of his money

That last expression is set equal to (1/3)x because David is left with 1/3 of his original money.

(3/4)(x-75) = (1/3)x
12*(3/4)(x-75) = 12*(1/3)x
9(x-75) = 4x
9x-675 = 4x
9x-4x = 675
5x = 675
x = 675/5
x = 135
David started off with $135

Check:
Start = 135
Buy the shirts: 135-75 = 60 dollars left
(1/4)*60 = 15 dollars spent on batteries
60-15 = 45 dollars at the end
45/135 = 1/3 of what he started with
The answer is confirmed.

Answer by mananth(16946) About Me  (Show Source):
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Let him have $x before shopping
75 on t shirt
x -75 Balance
1/4(x-75) on batteries
x-75 -1/4(x-75) =1/3 x
x-75 -x/4 +75/4 =x/3
Rearrange and simplify
x-7x/12 = 75+75/4
5x/12 = 225/4
5x = 225*12/4
5x= 225*3
x = 45*3
x= 135
He had $ 135 before shopping

Answer by ikleyn(52894) About Me  (Show Source):
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.
David spent $75 of his money on some t-shirts.
He spent 1/4 of the remaining money on some batteries.
Given that he was left with 1/3 of his original sum of money left,
how much money did David have at first?
~~~~~~~~~~~~~~~ 

Let x be the final amount;

then the starting amount was 3x, according to the problem.


After spending $75 on t-shirts, David left with (3x-75) dollars.


After spending 1/4 of remaining money on batteries, David remained with  %283%2F4%29%2A%283x-75%29  dollars.


        The problem says that  %283%2F4%29%2A%283x-75%29 = x.


Simplify and find x

    9x - 225 = 4x

    9x - 4x = 225

       5x   = 225

        x   = 225/5 = 45.


He was left with 45 dollars.

Hence, he started with 3*45 = 135 dollars.    ANSWER

Solved.



Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
David spent $75 of his money on some t-shirts. He spent 1/4 of the remaining money on some batteries. Given that he was left with 1/3 of his original sum of money left, how much money did David have at first?

Let initial amount David had, be D
After spending $75, he had D - 75 remaining
After spending ¼remainder, he then had: ¾remainder, or ¾(D  -  75), or %283D++-++225%29%2F4 remaining
Since after his spending "spree," his remainder was 1%2F3 of his initial amount, we then get:  
                                                                                         3(3D - 225) = 4D ----- Cross-multiplying
                                                                                            9D - 675 = 4D
                                                                                               - 675 = 4D - 9D
                                                                                               - 675 = - 5D
                                                                    Original amount David had, or