SOLUTION: Henry spent 1/4 of his money and an additional $3 on a number of DVDs. He then spent 3/5 of the remaining money and an additional $6 on a number of batteries. Given that he was lef
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Question 1184436: Henry spent 1/4 of his money and an additional $3 on a number of DVDs. He then spent 3/5 of the remaining money and an additional $6 on a number of batteries. Given that he was left with $24, how much money did Henry have at first? Answer by ikleyn(52797) (Show Source):
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Henry spent 1/4 of his money and an additional $3 on a number of DVDs.
He then spent 3/5 of the remaining money and an additional $6 on a number of batteries.
Given that he was left with $24, how much money did Henry have at first?
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It is a nice problem to be solved backward and explained accordingly.
First, let x be the remainder money amount after buying a number of DVDs.
Then for this amount of money you have this equation
x - = 24. (1)
To solve it, multiply everything in equation (1) by 5 to get
5x - (3x + 30) = 24*5
5x - 3x = 24*5 + 30
2x = 120 + 30 = 150
x = 150/2 = 75.
Thus you found that after buying a number of DVDs, the remainder was 75 dollars.
OK. It gives you NEXT EQUATION from the first part of the problem
M - = 75 (2)
where M is the unknown money amount Henry had at first.
From this equation, you get
= 75 + 3 = 78,
M = = 26*4 = 104.
ANSWER. At first, Henry had $104.
