Equations & Inequalities Game

The perimeter of the triangle shown is 17x units. The dimensions of the triangle are given in units. Which equation can be used to find the value of x?

• 17x = 30 + 7x

• 17x = 15 + 22x

• 17x = 7 + 30x

• 17x = 22 + 15x

Pool 1 contains 14.6 gallons of water. Stella will begin filling Pool 1 at a rate of 2.4 gallons per minute. Pool 2 contains 74.6 gallons of water. Jill will begin draining Pool 2 at a rate of 0.5 gallon per minute. After how many minutes will both pools contain the same amount of water? Round your answer to the nearest hundredth place.

• 14.6+2.4m = 74.6−0.5m

  m= 20.69

• 14.6-2.4m = 74.6−0.5m

  m= -20.69

• 14.6+2.4m = 74.6+0.5m

  m= 18.75

• 12.4m = -0.5m

  m= 0

At a store each notebook has a cost of x dollars. Which situation can be represented by this inequality: 5x < 3x + 2?

• The cost of 5 notebooks is greater than the cost of 3 notebooks plus a $2 pen.

• The cost of 5 notebooks is less than the cost of 3 notebooks with a $2-off coupon.

• The cost of 5 notebooks is less than the cost of 3 notebooks plus a $2 pen.

• The cost of 5 notebooks is $2 greater than the price of 3 notebooks.

Two customers spent the same total amount of money at a restaurant. The first customer bought 8 hot wings and left a $4 tip. The second customer bought 10 hot wings and left a $2.80 tip. Both customers paid the same amount per hot wing. How much does one hot wing cost at this restaurant in dollars and cents?

• $0.75

• $0.50

• $0.60

• $0.59

Bucket P and Bucket Q are both leaking water. Bucket P contains 750 mL of water and is leaking 8 mL per minute. Bucket Q contains 800 mL of water and is leaking 12 mL per minute. Which equation can find x, the number of minutes it will take for the two buckets to have the same amount of water?

• 750+8x = 800+12x

  -12.5 minutes

• 750-8x = 800-12x

  12.5 minutes

• -8x = 800-12x

  200 minutes

• 750+8x = 800-12x

  2.5 minutes

Jerry has a new job and earns a salary of $45,000. Victoria has a new job and earns a salary of $54,000. Jerry will receive a salary increase of $2,500 per year, and Victoria will receive a salary increase of $1,500 per year. Which equation can be used to find x, the number of years it will take Jerry to earn the same salary as Victoria?

• F: 45,000x + 2,500x = 54,000x + 1,500x

• G: 45,000x + 2,500 = 54,000x + 1,500

• H: 45,000 + 2,500x = 54,000 + 1,500x

• J: 45,000x + 2,500x = 54,000x + 1,500

Rectangle ABCD is shown with the dimensions given in units. The length of AB is greater than the length of AD. Which inequality represents this situation?

• 9x + 16 > 1.5x + 42

• 9x - 16 > 1.5x + 42

• 10.5x < 26

• 10.5x > 26

Gym A charges a registration fee of $75 plus a monthly fee of $35.75. Gym B charges a registration fee of $164 and $19.95 per month. After how many months would the total cost at Gym A and Gym B be the same?

• 10 Months

• 5 Months

• 7 Months

• None of the answers are correct.

Which of the following situations could be solved by using the inequality shown?

9 + 1.25x > 14 + 0.75x

• Park A charges an entrance fee of $9 plus $1.25 per ride. Park B charges $14 per ride and an entrance fee of $0.75. After how many rides will be the total charge at Park A Cost more than Park B?

• Danny finishes 1.25 homework problems every 9 minutes. Katie finishes 0.75 problems every 14 minutes. After how many minutes will Danny have completed more of his homework?

• Jake has $9 and spends $1.25 each day. Finley has $14 and spends $0.75 each day. After how many days will Jake have more money than Finley?

• Essence has run 9 miles and she runs 1.25 additional miles each day. Asia has run 14 miles and she runs 0.75 additional miles each day. After how many days will Essence have run more total miles than Asia?