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Example 5.33 from Elementary Algebra, 5.3 Solve Systems of Equations by Elimination
Solve Systems of Equations by Elimination: example 5.33
Joe stops at a burger restaurant every day on his way to work. Monday he had one order of medium fries and two small sodas, which had a total of 620 calories. Tuesday he had two orders of medium fries and one small soda, for a total of 820 calories. How many calories are there in one order of medium fries? How many calories in one small soda?
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. Step 2. Identify what we are looking for. We are looking for the number of
calories in one order of medium fries
and in one small soda.Step 3. Name what we are looking for. Let f = the number of calories in
1 order of medium fries.
s = the number of calories in
1 small soda.Step 4. Translate into a system of equations: one medium fries and two small sodas had a
total of 620 caloriestwo medium fries and one small soda had a
total of 820 calories.Our system is: Step 5. Solve the system of equations.
To solve the system of equations, use
elimination. The equations are in standard
form. To get opposite coefficients of f,
multiply the top equation by −2.Simplify and add. Solve for s. Substitute s = 140 into one of the original
equations and then solve for f.Step 6. Check the answer. Verify that these numbers make sense
in the problem and that they are
solutions to both equations.
We leave this to you!Step 7. Answer the question. The small soda has 140 calories and
the fries have 340 calories.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Malik stops at the grocery store to buy a bag of diapers and 2 cans of formula. He spends a total of $37. The next week he stops and buys 2 bags of diapers and 5 cans of formula for a total of $87. How much does a bag of diapers cost? How much is one can of formula?
How did it go?