1Cademy - Solving a Savings and Stock Interest Application Using a System of Equations

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Solving a Savings and Stock Interest Application Using a System of Equations

Apply the seven-step problem-solving strategy and a mixture table to solve an interest application involving two investments. Problem: Leon had $\$50{,}000$ to invest and hopes to earn $6.2\%$ interest per year. He will put some of the money into a stock fund that earns $7\%$ per year and the rest in to a savings account that earns $2\%$ per year. How much money should he put into each fund? 1. Read the problem. 2. Identify what to find: the amount to invest in each fund. 3. Name the unknowns. Let $s$ = the amount invested in stocks, and $a$ = the amount invested in the savings account. Organize into a table: / Fund / Principal ($) / Rate / Interest ($) / /---/---/---/---/ / Stocks / $s$ / $0.07$ / $0.07s$ / / Savings / $a$ / $0.02$ / $0.02a$ / / Total / $50{,}000$ / $0.062$ / $0.062(50{,}000)$ / 4. Translate into a system of equations: $\left\{\begin{array}{l} s + a = 50{,}000 \ 0.07s + 0.02a = 0.062(50{,}000) \end{array} ight.$ 5. Solve the system by elimination. Multiply the top equation by $-0.02$ : $-0.02s - 0.02a = -1{,}000$ $0.07s + 0.02a = 3{,}100$ Add the equations: $0.05s = 2{,}100$ $s = 42{,}000$ Substitute $s = 42{,}000$ into the first equation: $42{,}000 + a = 50{,}000$ $a = 8{,}000$ 6. Check the answer. $42{,}000 + 8{,}000 = 50{,}000$ $\checkmark$ $0.07(42{,}000) + 0.02(8{,}000) = 2{,}940 + 160 = 3{,}100$ $0.062(50{,}000) = 3{,}100$ $\checkmark$ 7. Answer the question. Leon should invest $\$42{,}000$ in the stock fund and $\$8{,}000$ in the savings account.

Updated 2026-05-25

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OpenStax Intermediate Algebra

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