Solving Equation & Inequality Word Problems

Marcella and Susie are running a race. Marcella runs at a rate of 15 feet per second while Susie only runs at a rate of 12 feet per second. If Susie gets a 48 feet head start, how long will it take for Marcella to pass her?

• 15x + 12x > 48, x > 16/9

• 15 + x > 12x + 48, x < -3

• 15x < 12x + 48, x < 16

• 15x > 12x + 48, x > 16

A rental car agency charges $30.00 per day plus per mile $0.15. Another rental car agency charges $36.00 per day plus $0.10 per mile. How many miles would have to be driven in one day for both rental agencies to cost the same amount to rent?

• 30 + 0.15x = 36 + 0.10x, x = 120

• 30 + 36 = 0.10x + 0.36x, x = 143.478261

• 30 - 0.15x = 36 - 0.10x, x = -120

• 36 - 30 = 0.36x + 0.10x, x = 13.043478

A local bakery has a daily operating cost of $1800 plus a cost of $10 per cake they make. If a cake sells for $15, which equation could be used to determine the minimum number of cakes, c, they must sell each day to earn a profit?

• 15c < 1800 + 10c

• 15c = 1800 + 10c

• 15c > 1800 + 10c

• 10c < 1800 + 15c

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value?

• 15x + 2.5 = 10x + 3

• 15 + 2.5x = 10 + 3x

• 15 - 2.5x = 10 - 3x

• 15 - 10 = 2.5x + 3x

Choose the situation that could represent the inequality:

15 - 10 = 2.5x + 3x

• Kasey has a gift card for $25. She buys a $15 CD and as many decals as she can buy with the rest of the gift card. How many decals can she buy?

• The school band has 25 people, and the theater class has 15 people. How many people must move from the band class to the theater class for the theater class to be as big or larger than the school band?

Which situation can be best represented by this equation?

8x + 2 = 12x

• Grayson ran at a constant rate of 8 miles per hour in a race. Kadence ran at a constant rate of 12 miles per hour in a race and started 2 miles in front of the starting point. What is x, the number of hours that Grayson and Kadence would have run in order for their distance to be the same?

• Bryan went to two different amusement parks. The first park charged $8 per hour and gave a 1% discount for showing student ID. The other park charged $12 per hour. What is x, the number of hours that Bryan would have to stay at each park for the price to be the same?

• Jesse played a game where he scored 10 points per hour. Ann played the game and won 12 points per hour. What is x, the number of hours that Jesse and Grayson would have scored for their points to be the same?

• Claire rode her bicycle on two different days. The first day she rode 8 miles per hour and started 2 miles from her house. The second day she started from her house and rode 12 miles per hour. What is x, the number of hours that Claire would have to drive for the distance from each day to be the same.