SOLUTION: Ally and Tony had a total of $44.00. After Ally spent one-quarter of her money and Tony spent $5.00 of his money, Ally had half the amount that Tony had. How much money did Tony ha

Question 921198: Ally and Tony had a total of $44.00. After Ally spent one-quarter of her money and Tony spent $5.00 of his money, Ally had half the amount that Tony had. How much money did Tony have at the beginning?
Please provide and Illustration, detailed solution and check for your answer.
Found 3 solutions by ewatrrr, Theo, MathTherapy:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
A + T = 44
A/4 = (T-5)/2
A = 2T - 10
(2T-10) + T = 44
3T = 54
T = $18 AND A= $26
And...checking
26/4 = 13/2
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
a = amount that ally had.
t = amount that tony had.

a + t = 44

this is what they started out with.

after ally spent 1/4 of her money, she had 3/4 * a left.

after tony spent 5 dollars of his money, he had t - 5 left.

after they both spent that money, ally had 1/2 the amount that tony had.

3/4 * a = 1/2 * (t-5)

multiply both sides of this equation by 4/3 to get:

a = 4/3 * 1/2 * (t-5)

simplify to get a = 2/3 * (t-5)

you know that a + t = 44

substitute 2/3 * (t-5) for a in this equation to get:

2/3 * (t-5) + t = 44

simplify to get 2/3 * t - 2/3 * 5 + t = 44

combine like terms to get 5/3 * t - 10/3 = 44

add 10/3 to both sides of this equation to get:

5/3 * t = 44 + 10/3

multiply both sides of this equation by 3/5 to get:

t = 3/5 * 44 + 3/5 * 10/3

simplify to get:

t = 132/5 + 2

simplify to get t = 132/5 + 10/5 = 142/5

you get t = 142/5 = 28.4

since a + t = 44, then a must be equal to 15.6 because 15.6 + 28.4 = 44

you have a = 15.6 and t = 28.4

tony had 28.4 dollars at the beginning.

ally spend 1/4 of her money, so alley has 3/4 * 15.6 = 11.7 left.

tony spent 5 dollars of his money, so tony has 28.4 - 5 = 23.4 left.

11.7 = 1/2 * 23.4 so ally now has 1/2 of what tony has left.

everything checks out so the solution is good.

Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

Ally and Tony had a total of $44.00. After Ally spent one-quarter of her money and Tony spent $5.00 of his money, Ally had half the amount that Tony had. How much money did Tony have at the beginning?
Please provide and Illustration, detailed solution and check for your answer.

Initial amount Tony had was: $
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