6.
Ana Maria had $28,000 to invest. She divided the money into three
different accounts. At the end of the year, she earned $1.160 in interest.
The annual yield on each of the three accounts was 3.5%. 4.25% and
4.75%. The amount of money in the 4.75% account was 75% of the
amount of money in the 3.5% account. Define the variables and write a
system of equations to represent the situation.
Answer:
x + y + z = 28,000
0.035x + 0.0425y + 0.0475z = 1160
z = 0.75x
Step-by-step explanation:
Let x = amount invested at 3.5%.
Let y = amount invested at 4.25%.
Let z = amount invested at 4.75%.
The total amount is $28,000.
Equation 1:
x + y + z = 28,000
The total interest is $1,160.
Equation 2:
0.035x + 0.0425y + 0.0475z = 1160
“The amount of money in the 4.75% account was 75% of the
amount of money in the 3.5% account.”
Equation 3:
z = 0.75x
The system of equations is:
x + y + z = 28,000
0.035x + 0.0425y + 0.0475z = 1160
z = 0.75x