Solving a Dual Student Loan Interest Application Using a System of Equations
Apply the seven-step problem-solving strategy and a mixture table to find the principal given the amount of interest earned. Problem: 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 $1{,}066. What was the principal for each loan? 1. Read the problem. 2. Identify what to find: the principal of each loan. 3. Name the unknowns. Let = the principal for the bank loan, and = the principal for the federal loan. Organize into a table: / Loan / Principal ($) / Rate / Interest ($) / /---/---/---/---/ / Bank / / 0.025 / 0.025b / / Federal / / 0.069 / 0.069f / / Total / 18{,}000 / / 1{,}066 / 4. Translate into a system of equations: \left\{\begin{array}{l} b + f = 18{,}000 0.025b + 0.069f = 1{,}066 \end{array} ight. 5. Solve the system using substitution. Solve the first equation for : Substitute into the second equation: To find , substitute into the first equation: 6. Check the answer. checkmark 0.025(4{,}000) + 0.069(14{,}000) = 100 + 966 = 1{,}066 checkmark 7. Answer the question. The principal for the bank loan was $4{,}000 and the principal for the federal loan was $14{,}000.
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Solving a Dual Student Loan Interest Application Using a System of Equations
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Solving a Dual Student Loan Interest Application Using a System of Equations
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