Question

Katy invests a total of $26,500 in two accounts paying 4% and 9% annual interest, respectively. How much was invested in each account if, after one year, the total interest was $1,510.00.

Answer 1

a = amount invested at 4%.

b = amount invested at 9%.

we know the total amount invested was $26500, thus a + b = 26500.

whatever% of anything is just (whatever/100) * anything.

how much is 4% of a? well, is just (4/100) * a, or 0.04a.

how much is 9% of b? well, is just (9/100) * b, or 0.09b.

we know the interest yielded for both amounts adds up to $1510, thus 0.04a + 0.09b = 1510.


`\bf \begin{cases} a+b=26500\implies \boxed{b}=26500-a\\ 0.04a+0.09b=1510\\ ----------------\\ 0.04a+0.09\left( \boxed{26500-a} \right)=1510 \end{cases} \\\\\\ 0.04-0.09a+2385=1510\implies -0.05a=-875 \\\\\\ a=\cfrac{-875}{-0.05}\implies a=17500`

how much was invested at 9%? well, b = 26500 - a.