Question

You have $1000 to invest in two different accounts. To save the money you need for college, you need to average 5.7 percent interest. If the two accounts pay 4 percent and 6 percent interest, how much should you invest in each account?

$550 in 4%, $450 in 6%
$300 in 4%, $700 in 6%
$700 in 4%, $300 in 6%
$150 in 4%, $850 in 6%

Answer 1

9514 1404 393

Answer:

$150 in 4%, $850 in 6%

Explanation:

The fraction that must earn the highest rate is ...

(5.7 -4.0)/(6.0 -4.0) = 1.7/2 = 0.85

That is 0.85 × $1000 = $850 must be invested at 6%. Matches the last choice.

_____

If you let x represent the amount that must earn 6%, then the total interest earned must be ...

x·6% +(1000 -x)·4% = 1000·5.7%

x(6 -4) = 1000(5.7 -4) . . . . . . multiply by 100, subtract 4·1000

x = 1000·(5.7 -4)/(6 -4) = 850 . . . . as above