Linear Equations and Inequalities Word Problems

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? Identify the equation that models this situation.

• 12 - 0.5x = 18 - 2x

• 12 + 0.5x = 18 + 2x

• 12x - 0.5 = 18x - 2

• 12 - 6x = 18 - 2x 

Tags

CCSS.8.EE.C.7B

Triniti had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets. Which inequality represents her situation?

• 200 + 25x ≥ 500

• 500 + 25x ≥ 200

• 500 - 25x ≥ 200

• 500 - 25x ≤ 200

Tags

CCSS.7.EE.B.4B

Peyton was given a $40 gift card to her local coffee shop. She went to the coffee shop four times and purchased the same thing each time. If she has $7.08 left on her gift card, what was the cost of her purchase each time she went to the coffee shop?

• 40 - 4c = 7.08

• 4(7.08) + c = 40

• 40 + 4c = 7.08

Tags

CCSS.HSA.CED.A.3

Solve

• n < 6

• n > 6

• n < 14

• n > 14

Tags

CCSS.7.EE.B.4B

Kate is selling bracelets and earrings on Etsy to make money for summer vacation. The bracelets (x) cost $2 and earrings (y) cost $3. She needs to make at least $100, but can only make up to 40 pieces of jewelry. Which inequalities represent this situation?

• 2x + 3y > 100

  x + y ≤ 40

• 100x + 2y > 3

  x + y ≤ 40

• 100x + 40y > 100

  3x + 2y ≤ 40

• 3x + 2y > 100

  x + y ≤ 40

Which situation can be represented by the inequality
15 + 6x ≤ 100?

• Lazer Zone charges $15 plus $6 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $6 plus $15 per person. If Andrea has a maximum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $15 plus $6 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

• Lazer Zone charges $6 plus $15 per person. If Andrea has a minimum of $100 to spend, how many people can Andrea invite to play laser tag?

Tags

CCSS.7.EE.B.4B

Joan needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

• 5x + 10 ≥ 100

• 5x - 100 ≥ 10

• 10x + 5 ≤ 100

• 5x + 10 > 100

Tags

CCSS.7.EE.B.4B

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

• 125x + 55 ≤ 600

• 125x + 55 ≥ 600

• 125x + 55 > 600

• 125x + 55 < 600

Tags

CCSS.7.EE.B.4B

Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• 10x + 1.50 ≥ 40

• 1.50x + 10 ≤ 40

• 1.50x + 10 <40

• 10x + 1.50 < 40

Tags

CCSS.7.EE.B.4B

Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat.  Write an equation for C, the total cost, to rent the boat for h hours.

• h = 2C + 15

• C = 15h + 2

• h = 15C + 2

• C = 2h + 15

Tags

CCSS.HSF-BF.A.1A