A recently retired couple has $150,000 to invest to supplement their social security. The invested some of it in an account that paid 10% simple interest per year, and they invested the rest in an account that paid 5% simple interest per year. After one year, they received a total of $12,000 in interest. How much did they invest in each account?

Step 1; Assume x is the amount of money put into the account that pays 10% simple interest and y the amount of money put into the account that pays 5% simple interest. It is given that the couple invests $150,000 in total. so

x + y = 150,000, take this as equation 1.

So x is the amount of money put into the account that gives 10% of x back and y is the amount of money into the account that gives 5% of y back. Both accounts give back $12,000. So,

0.10x + 0.05y = 12,000, take this as equation 2.

Step 2; Now we solve these equations.

Equation 1 can also be, y = 150,000 - x, take this as equation 3.

Substitute equation 3 in 2,

0.10x + 0.05(150,000 - x) = 12,000,

0.10x + 7,500 - 0.05x = 12,000,

Taking the known values to the right and keeping the unknown x values on the right, we get

0.05x = 12,000 - 7,500,

0.05x = 4,500.

So x = 90,000

Substitute this is equation 1,

x + y = 150,000, y = 150,000 - x, y = 150,000 - 90,000 = 60,000.

So the old couple invests $90,000 into the account that gives 10% of simple interest and $60,000 into the account that gives 5% simple interest.