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Example 5.50 from Elementary Algebra, 5.5 Solve Mixture Applications with Systems of Equations
Solve Mixture Applications with Systems of Equations: example 5.50
Translate to a system of equations and solve:
Rosie owes $21,540 on her two student loans. The interest rate on her bank loan is 10.5% and the interest rate on the federal loan is 5.9%. The total amount of interest she paid last year was $1,669.68. What was the principal for each loan?
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Step 1. Read the problem. A chart will help us organize the information. Step 2. Identify what we are looking for. We are looking for the principal of each loan. Step 3. Name what we are looking for. Let the principal for the bank loan.
the principal on the federal loanThe total loans are $21,540. Record the interest rates as decimals
in the chart.Multiply using the formula l = Pr t to
get the Interest.Step 4. Translate into a system of
equations.
The system of equations comes from
the Principal column and the Interest
column.Step 5. Solve the system of equations
We will use substitution to solve.
Solve the first equation for b.Substitute b = −f + 21,540 into the
second equation.Simplify and solve for f. To find b, substitute f = 12,870 into
the first equation.Step 6. Check the answer in the
problem.We leave the check to you. Step 7. Answer the question. The principal of the bank loan is $12,870 and
the principal for the federal loan is $8,670.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Translate to a system of equations and solve:
Laura owes $18,000 on her student loans. The interest rate on the bank loan is 2.5% and the interest rate on the federal loan is 6.9 %. The total amount of interest she paid last year was $1,066. What was the principal for each loan?
How did it go?