SOLUTION: After spending $24 to buy a bag, Tom spent 1/4 of his remaining money on food and had 3/7 of his original amount of money left. How much did Tom have at first?

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Question 1185960: After spending $24 to buy a bag, Tom spent 1/4 of his remaining money
on food and had 3/7 of his original amount of money left. How much did
Tom have at first?
Found 3 solutions by josgarithmetic, Theo, MathTherapy:
Answer by josgarithmetic(39623)   (Show Source):
You can put this solution on YOUR website!
p, money at first

, literal translation

Multiply both sides by 28, or by 4*7.

.
.

Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
let x = the original amount.

24 = amount paid for bag.

x - 24 = remainder after buying bag for 24.

1/4 * (x - 24) = amount paid for food.

3/4 * (x - 24) = remainder after buying food.

this remainder is equal to 3/7 * the original amount = 3/7 * x.

you get:

3/7 * x = 3/4 * (x - 24)

multiply both sides of this equation by 7/3 to get

x = 3/4 * 7/3 * (x - 24)

simplify to get:

x = 21/12 * (x - 24)

simplify further to get:

x = 21/12 * x - 21/12 * 24.

simplify further to get:

x = 21/12 * x - 42

subtract x from both sides of the equation and add 42 to both sides of the equation to get:

42 = 21/12 * x - x

combine like terms to get:

42 = 21/12 * x - 12/12 * x = 9/12 * x

solve for x to get:

x = 12/9 * 42 = 56

the original amount is 56.
subtract 24 to get remainder after bag = 32
1/4 * 32 = amount paid for food = 8.
remainder after food = 24
24 = 3/7 * x = 3/7 * original amount.
solve for x to get:
x = 7/3 * 24 = 7 * 8 = 56.

solution is confirmed to be good.

solution is tom had 56 dollars at first.

Answer by MathTherapy(10555)   (Show Source):
You can put this solution on YOUR website!

After spending $24 to buy a bag, Tom spent 1/4 of his remaining money
on food and had 3/7 of his original amount of money left. How much did
Tom have at first?

Let amount at first be A
After spending $24, A - 24 was left
After spending ¼ of the remainder, ¾ of (A - 24), or was left
With the final remainder being of original amount = = , we then have:
21A - 18(28) = 12A ------- Multiplying by LCD, 28
- 18(28) = 12A - 21A
- 18(28) = - 9A
Original amount he had, or