Question

john is taking out student loans from two banks. the first bank offers 3% apr compounded annually. the second bank offers 8% apr compounded annually. john took out a combined total of $9000 in loans and the total interest for the first year was $600. let x represent the amount of money loaned at 3%. let y represent the amount loaned at 8%. a. we want to form a system of equations to model this situation. i. write an equation that models the relationship between the amounts loaned from each bank. ii. write an equation that models the relationship of the interests earned for the first year. b. solve the system of equations to determine how much was loaned from each bank. $ was loaned at 3% apr and $ was loaned at 8% apr. box 1: enter your answer as an equation. example: y

Answer 1

The relationship between the amounts loaned from each bank be, x + y = 9000

and the relationship between the interests earned for the first year be, 3x + 8y = 60000

Given, John is taking out student loans from two banks.

The first bank offers 3% apr compounded annually.

The second bank offers 8% apr compounded annually.

John took out a combined total of $9000 in loans and the total interest for the first year was $600.

Let x represent the amount of money loaned at 3%. let y represent the amount loaned at 8%. a.

(i) amount from first bank be, x

and the amount from second bank be, y

so, x + y = 9000

(ii) interest for the first year from first bank is,

3x/100

and the interest for the first year from second bank is,

8y/100

so, 3x/100 + 8y/100 = 600

3x + 8y = 60000

Hence, the relationship between the amounts loaned from each bank be, x + y = 9000

and the relationship between the interests earned for the first year be, 3x + 8y = 60000

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