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Example 5.47 from Elementary Algebra, 5.5 Solve Mixture Applications with Systems of Equations
Solve Mixture Applications with Systems of Equations: example 5.47
Translate to a system of equations and solve:
Carson wants to make 20 pounds of trail mix using nuts and chocolate chips. His budget requires that the trail mix costs him $7.60 per pound. Nuts cost $9.00 per pound and chocolate chips cost $2.00 per pound. How many pounds of nuts and how many pounds of chocolate chips should he use?
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. We will create a table to organize the information. Step 2. Identify what we are looking for. We are looking for the number of pounds of nuts
and the number of pounds of chocolate chips.Step 3. Name what we are looking for. Let the number of pound of nuts.
the number of pounds of chipsCarson will mix nuts and chocolate chips
to get trail mix.
Write in n and c for the number of pounds
of nuts and chocolate chips.
There will be 20 pounds of trail mix.
Put the price per pound of each item in
the Value column.
Fill in the last column usingNumber · Value = Total Value Step 4. Translate into a system of equations.
We get the equations from the Number
and Total Value columns.Step 5. Solve the system of equations
We will use elimination to solve the system.Multiply the first equation by −2 to eliminate c. Simplify and add. Solve for n. To find the number of pounds of
chocolate chips, substitute n = 16 into
the first equation, then solve for c.Step 6. Check the answer in the problem. Step 7. Answer the question. Carson should mix 16 pounds of nuts with
4 pounds of chocolate chips to create the trail mix.
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:
Greta wants to make 5 pounds of a nut mix using peanuts and cashews. Her budget requires the mixture to cost her $6 per pound. Peanuts are $4 per pound and cashews are $9 per pound. How many pounds of peanuts and how many pounds of cashews should she use?
How did it go?