Equations and Inequalities

Carnival M charges an entrance fee of $5.00 and $0.65 per ticket for the rides. Carnival P charges an entrance fee of $10.00 and $0.45 per ticket for the rides. How many tickets must be purchased in order for the total cost at Carnival M and Carnival P to be the same?

• 25

• 10

• 50

• 75

Find the value of x for the equation below:

-3x + 10 = 5x - 8

• x = 1

• x = 2.25

• x = -1.5

• x = 2

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

• 5.75

• 8.25

• 10.25

• 12.5

Frankie bought a new computer. He made an initial payment of $50 to the store, and he will pay $30 each month until the computer is paid off. Which equation represents the relationship between m, the number of monthly payments Frankie has made, and t, the total amount that Frankie has paid the store?

• t = 50m + 30

• t = 30m - 50

• t = 50m - 30

• t = 30m + 50

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?

• 3.5 + 25x < 7.5 + 17x

• 3.5 + 25x > 7.5 + 17x

• 3.5x + 25 < 7.5x + 17

• 3.5x + 25 > 7.5x + 17

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 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 by each class is the same?

• 3t + 350 = 2.5t + 225

• 350t + 2.5 = 225t + 3

• 2.5t + 350 = 3t + 225

• none of the above

Renting video games from Store S costs $2.50 per game, plus a monthly fee of $5.  Renting from Store T costs $5 per game, without a monthly fee.  Which inequality represents the situation in which renting from Store S costs less than renting from Store T?  

• 2.5v + 5 < 5v
• 2.5v + 5 > 5v
• 7.5v > 5v
• 7.5v < 5v

Which situation can be represented by the equation 340 + 5x = 650 - 8x

• Sierra has a bucket that originally contained 340 oz of water and is filling at a rate of 5 fl oz per minute.  Brian has a bucket that originally contained 650 oz of water that is being drained at a rate of 8 fl oz per minute.  What is x, the number of minutes that need to pass for the two buckets to contain the same amount of water?
• Sierra started a savings account with $340.  She is spending $8 per week.  Brian started his savings account with $650 and he is saving $5 per week.  After how many weeks will Brian and Sierra have the same amount of money?
• Sierra starts a canned food drive with 340 cans of food.  Brian has 650 cans.  If Sierra collects 8 cans per day and Brian collects 5 cans per day, after how many days will Brian and Sierra have the same number of cans?
• Sierra earns 345 points for every level that she completes on a video game.  Brian earns 642 points per level.  How many levels does Sierra need to complete before she has the same number of points as Brian?

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 per trophy and an 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 for Company P is less than the total cost of Company R?

• 3.5 + 25x < 7.5 + 17x

• 3.5 + 25x > 7.5 + 17x

• 3.5x + 25 < 7.5x + 17

• 3.5x + 25 > 7.5x + 17