Question 1112148: Anna, Jennifer, and Mia have certain sums of money. If Anna gives Jennifer $100, they will have the same amount; If Anna gives Mia $100, Mia will have twice as much as Anna; if Jennifer gives Mia $100, Mia will have 4 times as much as Jennifer. What sum has each?
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! let A be the amount Anna has, let J be the amount Jennifer has, and M be the amount Mia has, then
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1) A-100 = J+100
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2) M+100 = 2(A-100)
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3) M+100 = 4(J-100)
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set equations 2 and 3 equal to each other
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2(A-100) = 4(J-100)
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substitute for (A-100) from equation 1
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2(J+100) = 4(J-100)
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2J+200 = 4J-400
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2J = 600
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J = 300
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A-100 = 300+100
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A = 500
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M+100 = 2(500-100)
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M = 700
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Jennifer has $300, Anna has $500 and Mia has $700
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check answer
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If Anna gives Jennifer $100, they will have the same amount
:
(500-100) = 300+100
$400 = $400
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If Anna gives Mia $100, Mia will have twice as much as Anna
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(500-100) 700+100
Anna has $400 and Mia has $800
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if Jennifer gives Mia $100, Mia will have 4 times as much as Jennifer
:
(300-100) 700+100
Jennifer has $200 and Mia has $800
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