Question 506: First question:
Right now, Alan's mother is 4 times older than he is. In 4 years, she will be 3 times older than he is. How old are Alan and his mother right now?
Second question:
Kim is using a list of his friends' ages. He adds two of his friends' ages and gets 17. He multiplies the ages and gets 72. How old are his two friends?
I would appreciate your help. Thanks.
-- Mary
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website! First question:
Right now, Alan's mother is 4 times older than he is. In
4 years, she will be 3 times older than he is. How old are
Alan and his mother right now?
`
Let Alan's age be X
`
>>...Alan's mother is 4 times older than he is...<<
`
Mother's age = 4X
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>>...In 4 years,...<<
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` (Alan's age in 4 years) = X+4
(Mother's age in 4 years) = 4X+4
`
>>...In 4 years, she will be 3 times older than he is...<<
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(Mother's age in 4 years) = 3 times (Allen's age in 4 years)
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` ` ` ` ` ` ` ` ` ` `4X+4 = 3(X+4)
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Can you solve that? Answer: X = 8, Mother's age = 4×8 = 32.
`
Check:
>>...Right now, Alan's mother is 4 times older than he is...<<
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That's true because he is 8 and she is 4 times 8 or 32.
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>>...In 4 years, she will be 3 times older than he is...<<
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That's true because he will be 12 and she will be 3 times
12 or 36.
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-----------------------------------
`
Second question: Kim is using a list of his friends' ages.
He adds two of his friends' ages and gets 17. He multiplies
the ages and gets 72. How old are his two friends?
`
Let x be one friend's age and y be the other friend's age:
`
>>...He adds two of his friends' ages and gets 17...<<
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Translation:` x + y = 17
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>>...He multiplies the ages and gets 72...<<
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Translation:` ` `xy = 72
`
You have this system to solve
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` ` ` ` ` ` ` x + y = 17
` ` ` ` ` ` ` ` `xy = 72
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Solve the first equation for y
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` ` ` ` ` ` ` ` ` y = 17-x
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Substitute 17-x for y in the second equation:
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` ` ` ` ` ` ` ` ` xy = 72
` ` ` ` ` ` `x(17-x) = 72
` ` ` ` ` ` 17x - x² = 72
` ` ` -x² + 17x - 72 = 0
` ` ` `x² - 17x + 72 = 0
` ` ` (x - 9)(x - 8) = 0
` ` ` x - 9 = 0 or x = 9
` ` ` x - 8 = 0 or x = 8
`
`If x = 8, then y = 17-8 or 9
`If x = 9, then y = 17-9 or 8
`
`Either way, one of them is 8 and the other 9.
`
`Edwin
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