Ana María had $28,000 to invest. She divided the money into three different accounts. At the end of the year, she had made $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 variables and write systems of equations to represent the situation. Solve the system to determine how much was put into each account.

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

Answers to the system of equations:

The total amount in each account is:

x = $8,000

y = $14,000

z = $6,000

step-by-step explanation:

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2