Please help me in this Algebra homework

Question

Caleb invested $9,400 in two different accounts, where the first account paid an interest rate of 8%, and the second account paid an interest rate of 7%. At the end of the first year, he earned $712 in interest. How much was invested into each account?

Answer 1

Hey Ana, let's talk about how you'd start this problem. One good way is to give names/variables to the things you're trying to figure out, then see if you can rephrase the information in the problem in terms of those variables. At the end, we're asked how much was invested in each account, and we don't know, so let's start by giving those variables:

x: amount invested in first account

y: amount invested in second account

Now we can go back through the problem and see if we can translate the information in the problem into math.

"Caleb invested $9,400 in two different accounts" becomes x + y = 9400

"the first account paid an interest rate of 8%" means "0.08 * x" is the interest earned by the first account

"the second account paid an interest rate of 7%" means "0.07 * y" is the interest from the second account

"he earned $712 in interest" means the sum of the interest earned is 712, so 0.08*x + 0.07*y = 712

So we've managed to distill the information in the problem to 2 equations:

x + y = 9400

0.08*x + 0.07*y = 712

Do you know what to do next?