Question

Emma has money into savings accounts. One rate is 8% and the other is 12%. If she has $450 more in the 12% account and the total interest is $220 how much is invested in each savings account?

Answer 1

Let's say that the value invested in the account with a rate of 8% is "x", then the amount invested in the account with a rate of 12% is:

$x+450$

To calculate the total interest we need to calculate the interest of each individual account and sum them:

$\begin{gathered} \frac{8}{100}\cdot x=0.08\cdot x \\ \frac{12}{100}\cdot(x+450)=0.12\cdot x+54 \end{gathered}$

The total interest is the sum of the two expressions above:

$\begin{gathered} 220=(0.08\cdot x)+(0.12\cdot x+54) \\ 220=0.08\cdot x+0.12\cdot x+54 \\ 220-54=0.2\cdot x \\ 166=0.2\cdot x \\ 0.2\cdot x=166 \\ x=\frac{166}{0.2} \\ x=830 \end{gathered}$

The value invested in the account with 8% interest is 830, the one invested in the account with 12% interest is 1280.