Equations and Inequalities Review

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?

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?

Two eighth-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 $3.00 each and has already raised $225.

Which equation 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?

• Not here

Veronica is ordering trophies for her school. Company P charges $3.50 for each trophy and a one-time engraving fee of $25. Company R charges $7.50 for each trophy and a one-time engraving fee of $17. Which inequality can be used to find x, the minimum number of trophies that can be ordered so that the total charge at Company P is less than the total charge at Company R?

Renting video games from Store S costs $2.50 per game plus a monthly fee of $5.00. Renting video games from Store T costs $5.00 per game with no monthly fee. The monthly cost to rent video games depends on the number of video games, v, rented. Which inequality represents the situation when the monthly cost at Store S is less than the monthly cost at Store T?

• 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.

Which situation can be represented by this equation?

7x + 1 = 10x

• Brody ran a constant rate of 7 miles per hour in a race. Candice ran at a constant rate of 10 miles per hour in a race and started 1 mile in front of the starting point. What is x, the number of hours that Brody and Candice 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 the game and scored 10 points per hour. What is x, the number of hours that Brody and Candice would each have to play the game in order for their scores to be the same?

• Brody went to two different amusement parks. The first park charged $7 per hour and gave a 1% discount for showing a student ID. The other park charged $10 per hour. What is x, the number of hours that Bordy would have to stay at each park to have to pay the same amount?

• Brody rode his bicycle on two different days. The first day he rode 7 miles per hour and started 1 mile from his house. The second day he started from his house and rode 10 miles per hour. What is x, the number of hours that Brody would have to ride his bicycle to travel the same distance on both days?

Which situation can be represented by this equation?

340 + 5x = 650 - 8x

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

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

• Sierra started with 340 cans of food for a food drive. She collects 5 more cans every day. Brian started with 650 cans of food for the food drive. He collects 8 more cans every day. What is x, the number of days that need to pass in order for Sierra and Brian to have the same number of cans of food?

• Sierra earns 345 points on each level of a video game. Brian earns 642 points on each level of the same video game. What is x, the number of levels that Sierra and Brian would have to play in order for them to have an equal number of points?

Aquarium I contains 4.6 gallons of water. Louise will 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 min

• 125 min

• 25 min

• 50 min

What value of x makes this equation true?

12x - 15 = 6 - 3x