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Example 5.24 from Elementary Algebra, 5.2 Solve Systems of Equations by Substitution
Solve Systems of Equations by Substitution: example 5.24
Heather has been offered two options for her salary as a trainer at the gym. Option A would pay her $25,000 plus $15 for each training session. Option B would pay her $10,000 + $40 for each training session. How many training sessions would make the salary options equal?
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 you are looking for. We are looking for the number of training sessions
that would make the pay equal.Step 3. Name what we are looking for. Let Heather’s salary.
the number of training sessionsStep 4. Translate into a system of equations. Option A would pay her $25,000 plus $15
for each training session.Option B would pay her $10,000 + $40
for each training sessionThe system is: Step 5. Solve the system of equations.
We will use substitution.Substitute 25,000 + 15n for s in the second equation. Solve for n. Step 6. Check the answer. Are 600 training sessions a year reasonable?
Are the two options equal when n = 600?Step 7. Answer the question. The salary options would be equal for 600 training sessions.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Geraldine has been offered positions by two insurance companies. The first company pays a salary of $12,000 plus a commission of $100 for each policy sold. The second pays a salary of $20,000 plus a commission of $50 for each policy sold. How many policies would need to be sold to make the total pay the same?
How did it go?