Word Problems to Equations

Lenny makes $55,000 and is getting annual raises of $2,500. Karl makes $62,000, with annual raises of $2,000. What equation shows how long it will take for Lenny and Karl to make the same salary?

• 55,000x + 2,500 = 62,000x + 2,000
• 2,500x + 55,000 = 2,000x + 62,000
• 55,000 - 2,500x = 62,000 - 2,000x
• 55,000 + 2,000x = 62,000 + 2,500x

At one store a trophy costs $12.50. Engraving costs $0.40 per letter. At another store, the same trophy costs $14.75. Engraving costs $0.25 per letter. Write an equation for how many letters the costs will be the same.

• 12.50 + 0.40 = 14.75 + 0.25
• 12.50x + 0.40 = 14.75x + 0.25
• 12.50 + 0.40x = 14.75 + 0.25x
• 0.40x - 12.50 = 0.25x - 14.75

A twelve inch candle and an 18 inch candle are lit at 6pm. The 12 inch candle burns 0.5 inches every hour. The 18 inch candle burns two inches every hour. At what time will the two candles be the same height? Write an equation.

• 12 - 0.5x = 18 - 2x
• 12 + 0.5x = 18 + 2x
• 12x - 0.5 = 18x - 2
• 12 - 6x = 18 - 2x 

Container A has 200L of water, and is being filled at a rate of 6 liters per minute. Container B has 500L of water, and is being drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water? Write an equation.

• 200m + 6 = 500m - 6
• 6m + 200 = 6m + 500
• 200 + 6m = 500 - 6m
• 200 - 6m = 500 + 6m

UPS charges $7 for the first pound, and $0.20 for each additional pound. FedEx charges $5 for the first pound and $0.30 for each additional pound. How many pounds, p, will it take for UPS and FedEx to cost the same? Write an equation.

• 7p +0.20 = 5p + 0.30
• 0.20p + 7 = 0.30p + 5
• 7 - 0.20p = 5 - 0.30p
• 0.20p - 7 = 0.30p - 5

In 2010, Ohio's population was 11.4 million and increasing by 0.5 million each year. Michigan's population was 9.9 million and increasing by 0.6 million each year. What will the two states have the same population? Write an equation.

• 11.4 + 0.5x = 9.9 + 0.6x
• 11.4x - 0.5 = 9.9x - 0.6
• 0.5x - 11.4 = 0.6x - 9.9
• 11.4x + 0.5 = 9.9x + 0.6

On Saturday, you bowl at Mar Vista Bowl, where renting shoes costs $2 and each game bowled is $3.50. On Sunday, you bowl at Pinz, where the shoe rental is $5 and each game bowled is $3.25. If you spent the same amount each day, how many games were bowled? Write an equation and solve.

• 3 games
• 12 games
• 10 games
• Infinite games

A handyman charges $150 plus $25 per hour for house painting. A painter charges $55 per hour. How many hours would a job have to take for the handyman's fee and the painter's fee to be the same? Write an equation and solve.

• 5 hours
• 3 hours
• 4 hours
• 1 hour

Solve for y:
-5 - 7y = -20y + 34

• y = 3
• y = 1
• y = 0.67
• y = 46

Solve for x:
19.2 x - 15 = 7.5x + 8.4

• x = 15.3
• x = 23.4
• x = 2
• x = 0