Before writing an inequality, it is easier to translate it first and then write it as an inequality.

Example: Nancy would like to have a birthday party at Golf and Go Putt-Putt Palace. The party will cost $4.50 for each person in attendance, plus a $55 deposit. How many people, p, can Nancy invite and keep the cost of the party below d dollars?

Translate each part of the problem and write an inequality.

Fill in the blanks on your own paper. When you are finished, click "Check Your Answer."

• A mathematical phrase representing "The party will cost $4.50 for each person, p, attending the party" is _____.
  
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  4.50p
• Remembering there is a deposit, the new mathematical phrase is _____.
  
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  4.50p + 55
• The phrase "keep the cost of the party below d dollars" is represented mathematically by _____.
  
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  d
• The inequality equation is: _____.
  
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  4.5p + 55 < d

Example: The glee club is selling flowers in order to raise money for competition uniforms. They are selling roses for $3 and sunflowers for $4. How many roses, r, and sunflowers, s, must they sell to raise at least $500 for the competition uniforms?

On your own paper, translate each part of the problem and write an inequality. When you are finished, click "Check Your Answer."

• A mathematical phrase representing "They are selling roses, r for $3" _____.
  
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  3r
• A mathematical phrase representing "sunflowers, s, for $4" _____.
  
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  4s
• A mathematical phrase representing the number of roses and the number of sunflowers is _____.
  
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  3r + 4s
• The phrase "to raise at least $500" is represented mathematically by _____.
  
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  ≥ 500
• The final inequality is _____.
  
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  3r + 4s ≥ 500

Now you are ready to try some. On your own paper, write the inequality for each problem situation.

Problem 1: Samantha is at the zoo with her sister's Girl Scout troop. She can buy candy bars for $2 each or bags of popcorn for $3 each to feed the girls a snack. Write an inequality that can be used to determine the number candy bars, c, and bags of popcorn, p, she can purchase if she only has $40?

Problem 2: Elena has a budget of d dollars to spend on clothes. The skirts she wants to buy are on sale for $19 each, including tax. Write an inequality that can be used to determine s, the maximum number of skirts Elena can buy if she has already spent $60 on a sweater?

Problem 3: Musa has set up a yard service because he needs to earn at least $500 to pay for his car insurance. He charges $25 to mow the yard and $8 per hour to weed flower beds. Write an inequality that can be used to determine x, the number of yards Musa must mow, and y, the number of flower beds he must weed in order to pay for his car insurance.

Click below to check your answers once you have completed all three problems.

Check Your Answer

Answer to problem 1: 2c + 3p ≤ 40

Answer to problem 2: 19s + 60 ≤ d

Answer to problem 3: 25x + 8y ≥ 500