Interpreting Inequalities

The temperature in Reklaw is 70°F and is decreasing at a rate of 2° per hour. The temperature in Sacul is 68°F and is decreasing at a rate of 1.5° per hour. Write an inequality to represent the number of hours until the temperature in Reklaw is lower than the temperature in Sacul.

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Roger and Novak are having a hot dog eating contest. Novak has consumed 7 hot dogs and Roger has consumed 8 hot dogs. From that point, Roger eats 3 hot dogs each minute while Novak eats 4 hot dogs per minute. Write an inequality to represent how many minutes, m, it will take Novak to eat as many or more hot dogs than Roger.

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Which situation can be represented by this inequality?

3x + 20 > 5x +10

• Jessie charges 3 dollars per hour plus a 20 dollar fee for babysitting. Joey charges 10 dollars per hour plus a 5 dollar gas fee to mow yards. When, in hours, will Jessie earn more than Joey?

• Maria is 20 feet from her house and walking at a rate of 3 feet per second. Jill started 10 feet from the house and is walking at a rate of 5 feet per second. At what time, in seconds, is Maria ahead of Jill?

• Donald reads a magazine at a rate of 3 pages per minute but started on page 20. Daisy started reading at page 10 and read at 5 pages per minute. When, in minutes will they be on the same page?

• At the beginning of soccer season, Jackson had already scored 20 goals. He is now scoring 3 goals per game. Nicholas is scoring 5 goals per game but started with only 10 goals. If x represents the number of games, after how many games will Nicholas have scored more total goals than Jackson?

Solve:

A taxicab company charges a flat fee of $5.50 plus an additional $1.25 per mile. How many miles would the taxi be driven if the cost was $15.50?

• 4 miles

• 3 miles

• 10 miles

• 8 miles

This symbol can be interpreted as 'is greater than or equal to'. What is another way of interpreting this symbol?

• is no more than

• is no less than

• is at most

• is less than

Penelope wants to have a party at an ice skating rink, but she has no more $100 to spend. The ice skating rink charges $50 for the rental fee and $5.50 per person. Interpret your solution.

• Penelope can invite no more than 9 people.

• Penelope can invite no more than 10 people.

• Penelope can invite more than 9 people.

• Penelope can invite more than 10 people.