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Example 5.49 from Elementary Algebra, 5.5 Solve Mixture Applications with Systems of Equations
Solve Mixture Applications with Systems of Equations: example 5.49
Translate to a system of equations and solve:
Adnan has $40,000 to invest and hopes to earn 7.1% interest per year. He will put some of the money into a stock fund that earns 8% per year and the rest into bonds that earns 3% per year. How much money should he put into each fund?
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 amount to invest in each fund. Step 3. Name what we are looking for. Let the amount invested in stocks.
the amount invested in bonds.Write the interest rate as a decimal for
each fund.
Multiply:
Principal · Rate · Time
to get the Interest.Step 4. Translate into a system of
equations.
We get our system of equations from
the Principal column and the
Interest column.Step 5. Solve the system of equations
Solve by elimination.
Multiply the top equation by −0.03.Simplify and add to solve for s. To find b, substitute s = 32,800 into the first equation. Step 6. Check the answer in the problem. We leave the check to you. Step 7. Answer the question. Adnan should invest $32,800 in stock and
$7,200 in bonds.Did you notice that the Principal column represents the total amount of money invested while the Interest column represents only the interest earned? Likewise, the first equation in our system, s + b = 40,000, represents the total amount of money invested and the second equation, 0.08s + 0.03b = 0.071(40,000), represents the interest earned.
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:
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?
How did it go?