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Example 3.58 from Elementary Algebra, 3.6 Solve Applications with Linear Inequalities
Brenda’s best friend is having a destination wedding and the event will last 3 days. Brenda has $500 in savings and can earn $15 an hour babysitting. She expects to pay $350 airfare, $375 for food and entertainment and $60 a night for her share of a hotel room. How many hours must she babysit to have enough money to pay for the trip?
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.
| Step 1. Read the problem. | |
| Step 2. Identify what we are looking for. | the number of hours Brenda must babysit |
| Step 3. Name what we are looking for.
Choose a variable to represent that quantity. |
Let the number of hours. |
| Step 4. Translate. Write a sentence that gives the information to find it. Translate into an inequality. |
The expenses must be less than or equal to the income.
The cost of airfare plus the cost of food and entertainment and the hotel bill must be less than or equal to the savings plus the amount earned babysitting. |
| Step 5. Solve the inequality. | |
| Step 6. Check the answer in the problem and make sure it makes sense.
We substitute 27 into the inequality. |
|
| Step 7. Write a sentence that answers the question. | Brenda must babysit at least 27 hours. |
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
Malik is planning a 6-day summer vacation trip. He has $840 in savings, and he earns $45 per hour for tutoring. The trip will cost him $525 for airfare, $780 for food and sightseeing, and $95 per night for the hotel. How many hours must he tutor to have enough money to pay for the trip?
How did it go?