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Angie has $20 to spend on juice boxes for her son’s preschool picnic. Each pack of juice boxes costs $2.63. What is the maximum number of packs she can buy?

seven packs

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Daniel wants to surprise his girlfriend with a birthday party at her favorite restaurant. It will cost $42.75 per person for dinner, including tip and tax. His budget for the party is $500. What is the maximum number of people Daniel can have at the party?

11 people

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Pete works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925?

Solution

Step 1. Read the problem. Step 2. Identify what we are looking for. the total sales needed for his variable pay option to exceed the fixed amount of $925 Step 3. Name what we are looking for. Choose a variable to represent that quantity. Let s = the total sales . Step 4. Translate Write a sentence that gives the information to find it. $500 plus 12% of total sales is more than $925. Translate into an inequality. Remember to convert the percent to a decimal. 500 + 0.12 s > 925 Step 5. Solve the inequality. 0.12 s > 425 s > 3,541. 66 Step 6. Check the answer in the problem and make sure it makes sense. If we round the total sales up to $4,000, we see that 500 + 0.12 ( 4,000 ) = 980 , which is more than $925. Step 7. Answer the question with a complete sentence. The total sales must be more than $3,541.67.

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Tiffany just graduated from college and her new job will pay her $20,000 per year plus 2% of all sales. She wants to earn at least $100,000 per year. For what total sales will she be able to achieve her goal?

at least $4,000,000

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Christian has been offered a new job that pays $24,000 a year plus 3% of sales. For what total sales would this new job pay more than his current job which pays $60,000?

at least $1,200,000

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Sergio and Lizeth have a very tight vacation budget. They plan to rent a car from a company that charges $75 a week plus $0.25 a mile. How many miles can they travel and still keep within their $200 budget?

Solution

Step 1. Read the problem. Step 2. Identify what we are looking for. the number of miles Sergio and Lizeth can travel Step 3. Name what we are looking for. Choose a variable to represent that quantity. Let m = the number of miles . Step 4. Translate Write a sentence that gives the information to find it. $75 plus 0.25 times the number of miles is less than or equal to $200. Translate into an inequality. 75 + 0.25 m 200 Step 5. Solve the inequality. 0.25 m 125 m 500 miles Step 6. Check the answer in the problem and make sure it makes sense. Yes, 75 + 0.25 ( 500 ) = 200 . Step 7. Write a sentence that answers the question. Sergio and Lizeth can travel 500 miles and still stay on budget.

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Taleisha’s phone plan costs her $28.80 a month plus $0.20 per text message. How many text messages can she use and keep her monthly phone bill no more than $50?

no more than 106 text messages

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Rameen’s heating bill is $5.42 per month plus $1.08 per therm. How many therms can Rameen use if he wants his heating bill to be a maximum of $87.50?

no more than 76 therms

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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