How to solve this problem step by step

Question

A total of $15,000 is invested in two accounts. One of the accounts earns 12% per year, and the other earns 10% per year. If the total interest earned in the first year is $1,600 , how much was invested in each account?

Answer 1

Assume a simple interest model.

Step 1. Turn words into algebra.

Let A₁ = Original amount invested in account 1

Let A₂ = Original amount invested in account 2

Let y₁ = Amount of interest earned in account 1 at the end of the first year

Let y₂ = Amount of interest earned in account 2 at the end of the first year

"A total of $15,000 is invested in two accounts" ~~> 15,000 = A₁ + A₂ (Equation 1)

"One of the accounts earns 12% per year [and we're only concerned about the first year]" ~~> 0.12A₁

"One of the accounts earns 10% per year [and we're only concerned about the first year]" ~~> 0.10A₂

"The total interest earned in the first year is $1,600" ~~> 1,600 = 0.12A₁ + 0.10A₂

Step 2. Recognize that the main equation to be solved 1,600 = 0.12A₁ + 0.10A₂ can be reduced to an equation with only one variable by using equation 1.

1,600 = 0.12A₁ + 0.10(15,000 - A₁)

Hope that helps.