Investment word problem

Question

Miguel invests $7600 in two different accounts. The first account paid 9 %, the second account paid 5 % in interest. At the end of the first year he had earned $496 in interest. How much was in each account?

Answer 1

Let a = the fraction in the 9% account

Let b = the fraction in the 5% account

then a + b = 1

the first account sum is a*7600(1.09)

the second account sum is b*7600(1.05)

the total of of both accounts must equal 7600 + 496 = 8096; substituting we have

8284a + 7980(1-a) = 8096

304a = 116. So, a = .3816. &. b =. .6184 which means that

.3816*7600 = $2900 is in the first account. & .6184*7600 = $4700 is in the second account.