Equations and Inequalities word problems

Two 8th grade classes are selling raffle tickets to raise money.

• One class is selling tickets for $2.50 each and has already raised $350.
• The other class is selling tickets for $3 each and has already raised $225.

Which equations can be used to find t, the number of tickets each class needs to sell so that the total amount raised is the same for both classes?

• 3t + 350 = 2.50t +225

• 350t + 2.50 = 225t + 3

• 2.50t + 350 = 3t + 225

• Not here

At a store each notebook has a cost of x dollars. Which situation can be represented by the 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.

Aquarium I contains 4.6 gallons of water. Louise begin filling Aquarium I at a rate of 1.2 gallons per minute.

Aquarium II contains 54.6 gallons of water. Isaac will begin draining Aquarium II at a rate of 0.8 gallon per minute.

After how many minutes will both aquariums contain the same amount of water?

• 148 minutes

• 125 minutes

• 25 minutes

• 50 minutes

Which situation can be represented by this equation?

340 + 5x = 650 - 8x

• Sierra has a bucket that originally contained 340 oz of water and is being filled at a rate of 5 oz per minute. Brain has a bucket that originally contained 650 oz of water and is being drained at a rate of 8 oz per minute. What is x, the number of minutes that need to pass in order for the 2 buckets to contain the same amount of water?

• Sierra started with savings of $340 and spends $8 every week. Brian started with savings of $650 and adds $5 every week. What is x, the number of weeks that need to pass for them to have the same amount of savings?

• Sierra started with 340 cans for a food drive. She collects 5 more cans every day. Brain started with 650 cans for the food drive and collects 8 more cans every day. What is x, the number of days before they will have the same number of cans?

• Sierra earns 345 points on each level of video game. Briain earns 642 points on each level of the same game. What is x, the number of levels they have to play before they will have an equal number of points?

Renting video games from Store S costs $2.50 per game plus a monthly fee of $5. Renting videos games from Store T costs $5 per game with not monthly fee. If v represents the number of video games rented, which inequality represents the when the monthly cost at Store S is less than the monthly cost at Store T?

• 2.5v + 5 < 5v

• 2.5v + 5 > 5v

• 7.5v < 5v

• 7.5v > 5v

Julie started with 20 pieces of gum and gave away x pieces. Conrad started with 35 pieces of gum and gave away twice as many pieces as Julie did. How many pieces of gum did Julie give away if they had the same number of pieces of gum left?

• 18

• 5

• 15

• 8

Helen had $330 in her savings account when Vince opened a savings account with zero dollars.

• Helen deposited $30 into her account each week for x weeks.
• Vince deposited $50 into his account each week for x weeks.
• The accounts did not earn interest.

Which inequality represents this situation when the amount of money in Helen's account was greater than the amount of money in Vince's account?

• 30x < 330 + 50x

• 50x > 330 + 30x

• 30x > 330 + 50x

• 50x < 330 + 30x

Which situation can be represented by this equation?

7x + 1 = 10x

• Brody ran at a constant rate of 7 miles per hour in a race. Candice ran at a constant rate of 10 miles per hour and started 1 mile in front of the starting point. What is x, the number of hours they both would have to run in order for their distance to be the same?

• Brody played a game where he scored 8 points per hour. Candice played a game where she scored 10 points per hour. What is x, the number of hours they both have to play in order for their scores to be the same?

• Amusement Park A charges $7 per hour and gives a 1% discount for showing a student ID. Amusement Park B charges $10 per hour. What is x, the number of hours you would have to stay at each park to have to pay the same amount?

• On day 1, you ride your bicycle 7 miles per hour and start 1 mile from your house. On day 2, you start from your house and ride 10 miles per hour. What is x, the number of hours you would have to ride to travel the same distance both days?

Jerry earns a salary of $45,000. Victoria 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?

• 45,000 + 1,500x = 54,000 + 2,500x

• 45,000x + 2,500 = 54,000x + 1,500

• 45,000 + 2,500x = 54,000 + 1,500x

• 45,000x + 2,500 = 54,000x + 1,500

The measures of 2 angles are (5x + 24) and (9x - 17). Which is the value of x if these 2 angles are congruent?

• 1.75

• 13.2

• 0.5

• 10.25