The couple invests $9,000 in the account that paid 10% simple interest and $6,000 in the account that paid 5% simple interest.
Step-by-step explanation:
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.
