3 equation problem

Question

Jovita divides 17,000 into three investments a savings account paying 6% annual interest, a bond paying 9% and a money fund paying 11%. The annual interest from the three accounts is 1540 and she has three times as much invested in the bond as in the saving account. what amaunt does she have invested in each account?

Answer 1

Let a,b,c be the fractions of the $17,000 that is invested in the savings, bond, & money fund respectively.

Let S1, S2, S3 be the total monies from the savings, bond, & money fund after the year with interest

We know that a+b+c=1, and S1+S2+S3=17000+1540=18540

We know that b=3a, and c=1-4a based on the condition of 3 times more in the bond account that the savings account.

S1 = a(17000)(1.06) =18020a

S2 = 3a(17000)(1.09) = 55590a

S3 = (1-4a)(17000)(1.11) = 18870-75480a Lets add the 3 equations and collect terms;

18540 = -1870a + 18870 Solving for a = .1765, b = .5294, c = .2940

So, $3000 was invested in the savings account, $9000 was invested in the bond account, & $5000 was invested in the money fund.