Inequality and Equations Word Problems

Sharon’s family budgeted $3000 for their vacation. Their budget consisted of $1850 for travel cost and $85 per day for hotel and other expenses. Which inequality will determine the amount of days Sharon’s family can stay on vacation?

• 1850 + 85x < 3000

• 1850 – 85x > 3000

• 1850 + 85x < 3000

• 1850 – 85x > 3000

I can join video club A for $25.00 and rent videos for $1.00 each. Or, I can join video club B for $15.00 and rent videos for $2.00 each. Write an equation that could be used to determine how many rentals would be needed for the price to be equal.

• 25 - x = 15 - 2x
• 25 + 15 = x + 2x
• 25x + 1 = 15x + 2
• 25 + x = 15 + 2x

Brandon has at most $58 to spend on clothes. The shirts he wants to buy are on sale for $9 each, and the pair of pants he wants costs $21. All prices include tax. Which inequality could be used to determine s, the maximum number of shirts Brandon can buy if he also buys the pair of pants?

• 21s + 9 < 58

• 9s + 21 ≤ 58

• 30s < 58

• 9s – 21 ≤ 58

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. Which equation could be used to determine 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
• 30 - 0.15x = 36 - 0.10x
• 30 + 36 = 0.10x + 0.36x
• 36 - 30 = 0.36x + 0.10x

Samuel has to spend at least $35 on movie rentals and snacks for the weekend in order to win free tickets to the movies. He spends $12 on popcorn and soda. If the movie store rents DVDs for $4 each, which inequality models n, the number of DVDs Samuel has to rent?

• 4n – 12 < 35

• 12n+4 < 12

• 35 – 4n > 12

• 4n + 12 > 35

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

Ms. Campos has no more than $5000 for their vacation. Her expenses consisted of $2300 for travel cost and $120 per day for hotel and other expenses. Which inequality will determine the amount of days Ms. Campos can stay on vacation?

• 2300 + 120x < 5000

• 2300 – 120x > 5000

• 2300 + 120x < 5000

• 2300 – 120x > 5000

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal? 

• 150x + 24 = 180 + 20x
• 150 + 24x = 180 + 20x
• 180 - 150 = 24 x + 20x
• 150 - 24x = 180 - 20x

Hotdog hut sells hotdogs for $4 each. For $15 per month, you can purchase a discount card which makes the hotdogs $2 each. Which inequality below could be used to find how many hotdogs (h) you would need to eat in a month to make the discount card a good deal?

• 4h > 15 + 2h

• 4h > 15h + 2

• 4h < 15 + 2h

• 4h < 15h + 2

Mary has been offered two jobs. Job A has a starting salary of $36,000 and a raise of $1500 every year. Job B has a starting salary of $29,000 and a raise of $2500 every year. Write an equation to determine how many years would Mary's salary be the same at both companies. 

• 36,000x + 1,500 = 29,000x + 2,500
• 36,000 - 29,000 = 1,500x + 2,500x
• 36,000 - 1,500x = 29,000 - 2,500x
• 36,000 + 1,500x = 29,000 + 2,500x