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

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Solving a Dual 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: Julius invested $\$7{,}000$ into two stock investments. One stock paid $11\%$ interest and the other stock paid $13\%$ interest. He earned $12.5\%$ interest on the total investment. How much money did he put in each stock? 1. Read the problem. 2. Identify what to find: the amount invested in each stock. 3. Name the unknowns. Let $x$ = the amount invested at $11\%$ , and $y$ = the amount invested at $13\%$ . Organize into a table: / Fund / Principal ($) / Rate / Interest ($) / /---/---/---/---/ / 11% Stock / $x$ / $0.11$ / $0.11x$ / / 13% Stock / $y$ / $0.13$ / $0.13y$ / / Total / $7{,}000$ / $0.125$ / $0.125(7{,}000)$ / 4. Translate into a system of equations: $\left\{\begin{array}{l} x + y = 7{,}000 \ 0.11x + 0.13y = 0.125(7{,}000) \end{array} ight.$ 5. Solve the system by elimination. Multiply the top equation by $-0.11$ : $-0.11x - 0.11y = -770$ $0.11x + 0.13y = 875$ Add the equations: $0.02y = 105$ $y = 5{,}250$ Substitute $y = 5{,}250$ into the first equation: $x + 5{,}250 = 7{,}000$ $x = 1{,}750$ 6. Check the answer. $1{,}750 + 5{,}250 = 7{,}000$ $\checkmark$ $0.11(1{,}750) + 0.13(5{,}250) = 192.5 + 682.5 = 875$ $0.125(7{,}000) = 875$ $\checkmark$ 7. Answer the question. Julius invested $\$1{,}750$ at $11\%$ and $\$5{,}250$ at $13\%$ .

Updated 2026-05-25

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OpenStax Intermediate Algebra

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