Writing and Solving Equations and Inequalities

Fred buys a binder for $4.50 and six reams of paper. Latasha buys an ink cartridge for $17.50 and four reams of paper. Both spend the same amount. What is the price of one ream of paper?

• $13.00

• $11.00

• $6.50

• $1.30

There are two rival cab companies. Cab Company Q charges a $2.50 initial fee and $0.15 per mile. Cab Company R charges an initial fee of $1.00 and $0.20 cents per mile. After how many miles do both cab companies charge the same amount?

• 10

• 50

• 30

• Not here

Printing company A prints calendars for $3 each and a setup fee for $46. Printing company B prints calendars for $5 each and has a setup fee of $20. Which inequality would be used to determine when company A is less than company B?

• 3x+46 < 5x+20

• 3x+46 > 5x+20

• 49x < 25x

• 3x+20 < 5x+46

Jack and Jill purchased cell phones. Jack signed up for a plan that charges a fee of $24.00 plus $0.08 every minute she talks. Jill's plan charges a fee of $10.00 plus $0.15 every minute she talks. Which inequality could be used to determine when Jill's cell phone plan costs more than Jack's cell phone plan?

• 24m+0.08m > 10m+0.15m

• 24+0.08m < 10+0.15m

• 24+0.08m > 10+0.15m

• 24m+0.08m < 10m+0.15m

Marie heated water in a beaker. When she began, the water had a temperature of 40 degrees, and she heated it a rate of 2.5 degrees per minute. Kathy heated water in a different beaker. When she began, the water had a temperature of 50 degrees, and she heated it at a rate of 1.5 degrees per minute. Which equation could be used to determine how many minutes passed before the water temperature in both beakers was the same?

• 2.5x+40=1.5x+50

• 2.5x+1.5x=40+50

• 2.5x+50=1.5x+40

• 40-2.5x=50-1.5x

What is the value of z that makes the equation 6z-12=2z+60 true?

• 18

• 9

• 12

• 6

What value of k makes the equation 8k-32=4k+4 true?

• 9

• -7

• -3

• 3

Camie and Jorge each begin saving money for a new computer. Camie saves $5 per week plus $50 she receives for her birthday. Jorge saves $7 per week. Which of the following can be used to find w, the number of weeks until Jorge has saved at least the same amount as Camie?

• 7w = 5w+50

• 50+5w < 7w

• 5w+50 ≥ 7w

• 7w ≥ 5w+50

Liam and Harper are racing on a track. Liam runs 4 miles per hour and gets a 0.25 mile head start. Harper runs 4.5 miles per hour. If Harper and Liam run the same distance, how many hours, x, do they run?

• 4x+0.25 = 0.5x

• 4x+0.25 = 4.5x

• 4x+0.25 = 3.5x

• 4x-0.25 = 3.5x

At one point during the summer, Marsha has read 500 pages of her summer reading assignment, and Jan has read 460 pages. Marsha reads 20 pages per week for the remainder of the summer, and Jan reads 30 pages per week for the remainder of the summer. How many weeks, w, will it take before the girls have read the same number of pages?

• 500+30w = 460+2w

• 30+500w = 20+460w

• 20+500w = 30+460w

• 500+20w = 460+30w