how much was invested in each mutual​ fund?

Question

An investor invested a total of $3,700 in two mutual funds. One fund earned a 5% profit while the other earned a 2% profit. If the investor's total profit was $134, how much was invested in each mutual fund?

Answer 1

it doesn't state how long the money is invested so I will assume 1 year!

The sum of the 2 investments will result in $3834 after a year

Let a = fraction invested in the 5% fund and b = the fraction invested in the 2% fund. Note a + b = 1

then 3700a(1.05) + 3700b(1.02) = 3834

3700a(1.05) + (1-a)3700(1.02) = 3834

3885a + 3774 - 3774a = 3834

111a = 60

a = .54 and b = .46

So, .54(3700) = $1998 in the 5% fund and .46(3700) = $1702 in the 2% fund.