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Example 3.57 from Elementary Algebra, 3.6 Solve Applications with Linear Inequalities
Solve Applications with Linear Inequalities: example 3.57
Elliot has a landscape maintenance business. His monthly expenses are $1,100. If he charges $60 per job, how many jobs must he do to earn a profit of at least $4,000 a month?
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. the number of jobs Elliot needs Step 3. Name what we are looking for. Choose a variable to represent it. Let the number of jobs. Step 4. Translate Write a sentence that gives the information to find it. $60 times the number of jobs minus $1,100 is at least $4,000. Translate into an inequality. Step 5. Solve the inequality. Step 6. Check the answer in the problem and make sure it makes sense.
If Elliot did 90 jobs, his profit would be , or . This is more than .Step 7. Write a sentence that answer the question. Elliot must work at least 85 jobs.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Caleb has a pet sitting business. He charges $32 per hour. His monthly expenses are $2,272. How many hours must he work in order to earn a profit of at least $800 per month?
How did it go?