Algebra question

Question

Jacob invests $10700 in two different accounts. The first account paid 14 %, the second account paid 3 % in interest. At the end of the first year he had earned $948 in interest. How much was in each account?

Answer 1

948/10700 = about 8.86%

some invested at 14%

the rest invested at 3%

as 8.86 is roughly the average of 14 and 3 = 17/2 = 8.5

roughly half is invested at each, slightly more at 14, as 8.86 is closer to 14 than to 3

.14x + .03(10700-x) = 948

.14x - .03x = 948 - .03(10700)

.11x = 948 - 321 = 627

x = 627/.11 = 57/.01 = $5700 invested at 14%

10700-5700 = $5000 invested at 3%