Heidi T. answered • 07/22/20

MS in Mathematics, PhD in Physics, 7+ years teaching experience

There are three pools of money - n invested at 5%, m invested at 4.5%, and q invested at 3.5%. The interest on any one of these pools is I = R x P where I is the interest, R is the interest rate, and P is the principle.

n + m + q = 35,000 (given) and n = q (given), so 2n + m = 35000

since m is the desired quantity, solve the above for n: n = (35000 - m)/2

The total interest is the sum of the interest of the individual amounts invested:

I = 1510 = n(0.05) + m(0.045) + n(0.035) = 0.085 n + 0.045 m replace n with the equation found above:

1510 = (0.085)(35000 - m)/2 + (0.045)m

solve for m:

multiply both sides of the equation by 2 to eliminate the fraction:

3020 = (0.085)(35000) - (0.085)m + (0.090)m

Group like terms and reduce:

3020 - 2975 = (0.005)m

Solve for m:

m = 45/(0.005) = 9000

Answer: $9000 are invested at 4.5%