Solving Inequalities Word Problems

Ross and Chandler go to Taco Land and order sodas for a total of $3.50. They also want to order some tacos (of course), which cost $1.75 each. If they have $20, how many tacos can they buy? Which inequality best represents the situation.

• 3.50 + 1.75t > 20

• 1.75 + 3.50t ≤ 20

• 3.50 + 1.75t ≥ 20

• 1.75t + 3.50 ≤ 20

Tyler has no more than $20 in his bank account.

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I have fewer than 100 students to teach each day.

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Less Than

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Write this mathematical sentence using algebra:

7 is subtracted from a number y. Then the result is multiplied by 3. The final answer is less than or equal to 12.

Write this mathematical sentence using algebra:

A number z is multiplied by 4. Then 8 is subtracted from the result. The final answer is greater than or equal to 28.

Gloria starts with five times as much money as Hamish. Gloria gives $8 to Hamish, and then Hamish has more money than Gloria. If Hamish starts with $h, then which of the following is a correct inequality for h?

• -15

• 6

• -2

• 9

Renting games online from Netwii costs $3.33 per game  with no monthly fee.  Renting games online from HDO costs $2.00 per game plus a monthly fee of $10.00.
Which inequality represents the situation when the monthly cost at Netwii is more than the monthly cost at HDO?

• 3.33v > 2v + 10

• 3.33v + 10 > 2v 

• 3.33v < 2v + 10

• 3.33v + 10 < 2v

The inequality shown below represents fees for two different apartments. 500x + 700 < 650x + 200 Which situation below does this inequality represent?

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is equal to Apartment A charging $650 per month with a $200 deposit.

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is greater than Apartment A charging $650 per month with a $200 deposit.

• Apartment A charges a $700 per month and then $500 deposit. Apartment B is greater than Apartment A charging $650 deposit with $200 per month.

• Apartment A charges a $700 deposit and then $500 per month. Apartment B is less than Apartment A charging $650 per month with a $200 deposit.