<< Chapter < Page Chapter >> Page >

A common goal of most businesses is to make a profit. Profit is the money that remains when the expenses have been subtracted from the money earned. In the next example, we will find the number of jobs a small businessman needs to do every month in order to make a certain amount of profit .

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?

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 j = 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. 60 j 1100  ≥ 4,000 Step 5. Solve the inequality. 60 j 5,100 j 85 jobs Step 6. Check the answer in the problem and make sure it makes sense. If Elliot did 90 jobs, his profit would be 60 ( 90 ) 1,100 , or $4,300. This is more than $4,000. Step 7. Write a sentence that answers the question. Elliot must work at least 85 jobs.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

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?

at least 96 hours

Got questions? Get instant answers now!

Felicity has a calligraphy business. She charges $2.50 per wedding invitation. Her monthly expenses are $650. How many invitations must she write to earn a profit of at least $2,800 per month?

at least 1,380 invitations

Got questions? Get instant answers now!

Sometimes life gets complicated! There are many situations in which several quantities contribute to the total expense. We must make sure to account for all the individual expenses when we solve problems like this.

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?

Solution

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 h = the number of hours . Step 4. Translate Write a sentence that gives the information to find it. 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. Translate into an inequality. $ 350 + $ 375 + $ 60 ( 3 ) $ 500 + $ 15 h Step 5. Solve the inequality. 905 500 + 15 h 405 15 h 27 h h 27 Step 6. Check the answer in the problem and make sure it makes sense. We substitute 27 into the inequality. 905 500 + 15 h 905 500 + 15 ( 27 ) 905 905 Step 7. Write a sentence that answers the question. Brenda must babysit at least 27 hours.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

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?

at least 23 hours

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask