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Answer to Question #4554 in Calculus for ong

Question #4554
Amy had $214 more than her brother.After their father gave Amy $85 and her brother $66,Amy had twice as much money as her brother.How much did Amy have at first?
Expert's answer
Let's sign Amys money by A and her brothers money by B. Hence,

A = B + 214 - at first
A + 85 = 2(B + 66) - after their father gave Amy $85 and her brother $66

Let's solve this system of equations. We'll substitute A from them first equation into the second:

B + 214 + 85 = 2(B + 66)
B + 299 = 2B + 132
So, B = 167.
From the first equation we'll receive: A = 167 + 214 = 381.
So, Amy had $381 at first.

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