Solving and Writing Equations and Inequalities Review

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?

• 2 hours

• 3 hours

• 4 hours

• 5 hours

Which situation can be represented by the equation 
1500 - 50x = 2000 - 100x

• There are two water tanks in the city.  One tank has 1500 gallons and gains 50 gallons each hour.  The other tank has 2000 gallons and gains 100 gallons each hour.  When will the tanks have the same amount of water?

• There are two water tanks in the city.  One tank has 1500 gallons and loses 50 gallons each hour.  The other tank has 2000 gallons and gains 100 gallons each hour.  When will the tanks have the same amount of water?

• There are two water tanks in the city.  One tank has 1500 gallons and loses 50 gallons each hour.  The other tank has 2000 gallons and loses 100 gallons each hour.  When will the tanks have the same amount of water?

• There are two water tanks in the city.  One tank has 1500 gallons and loses 50 gallons each hour.  The other tank has 2000 gallons and loses 100 gallons each hour.  When will the bigger tank have more water?

Solve for x

• x = 16

• x = 4

• x = 6

• x = 2

Solve the equation
4x - 5x + 9 =5x - 9

• x = -3

• x = 9

• x = 3

• x = -9

7 + 6x - 7x = 3x - 2x - 5

• x = 6

• x = -16

• x = -5

• x = 4

-8x - 8 + 3x - 6 = -3x + 2

• x = -8

• x = 8

• x = 2

• x = -2

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

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

• 3 hours

• 4 hours

• 1 hour

• 2 hours

Select the situation that could be modeled by: 12 + 5x = 18+3x

• Derek charges a base fee of $12 to walk a dog plus $5 per hour. Darla charges a base fee of $18 plus $3 an hour to walk a dog. After how many hours would they make the same amount of money?

• Andy buys 12 sodas for $5 each. Alex buys 18 sodas for $3 each. If they each spent the same amount, how much did they spend?

• Brian charges $12 for a hat and $5 per shirt. Blake buys 3 hats and 18 shirts. How many hats and shirts must they sell to make the same amount of money?

• Charlie sells dozens of eggs for $5.  Calvin sells a dozen and a half eggs for $3 each.  How many do they have to sell to make the same amount of money?

Solve.
.5x - 1 = .25x + 2

• x = 3

• x = -12

• x = 12

• x = -3