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Example 5.48 from Elementary Algebra, 5.5 Solve Mixture Applications with Systems of Equations
Solve Mixture Applications with Systems of Equations: example 5.48
Translate to a system of equations and solve:
Sasheena is a lab assistant at her community college. She needs to make 200 milliliters of a 40% solution of sulfuric acid for a lab experiment. The lab has only 25% and 50% solutions in the storeroom. How much should she mix of the 25% and the 50% solutions to make the 40% solution?
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 figure may help us visualize the situation, then we
will create a table to organize the information.Sasheena must mix some of the 25%
solution and some of the 50% solution
together to get 200 ml of the 40% solution.Step 2. Identify what we are looking for. We are looking for how much of each solution
she needs.Step 3. Name what we are looking for. Let number of ml of 25% solution.
number of ml of 50% solutionA table will help us organize the data.
She will mix x ml of 25% with y ml of
50% to get 200 ml of 40% solution.
We write the percents as decimals in
the chart.
We multiply the number of units times
the concentration to get the total
amount of sulfuric acid in each solution.Step 4. Translate into a system of
equations. We get the equations from
the Number column and the Amount
column.Now we have the system. Step 5. Solve the system of equations.
We will solve the system by elimination.
Multiply the first equation by −0.5 to
eliminate y.Simplify and add to solve for x. To solve for y, substitute x = 80 into the
first equation.Step 6. Check the answer in the problem. Step 7. Answer the question. Sasheena should mix 80 ml of the 25% solution
with 120 ml of the 50% solution to get the 200 ml
of the 40% solution.
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:
LeBron needs 150 milliliters of a 30% solution of sulfuric acid for a lab experiment but only has access to a 25% and a 50% solution. How much of the 25% and how much of the 50% solution should he mix to make the 30% solution?
How did it go?