Lesson 7: Linear inequality word problems

Kayla wants to visit a friend that lives 8 km away. She’ll ride the subway as far as she can before walking the rest of the way. She needs to buy an access pass for $5.50, and there’s a fee of $1.25 per stop

Kayla doesn’t want to spend more than $15, so she wants to know the largest number of stops she can afford. Let s represent the number of stops she buys (make inequality only)

5.50 + 1.25s is greater than or equal to 15

Kayla wants to visit a friend that lives 8 km away. She’ll ride the subway as far as she can before walking the rest of the way. She needs to buy an access pass for $5.50, and there’s a fee of $1.25 per stop

Kayla doesn’t want to spend more than $15, so she wants to know the largest number of stops she can afford. Let s represent the number of stops she buys (make inequality, then solve)

7

Translate: “more than c” “higher than c” “greater than c”

Means > c

Translate: “less than c” “lower than c”

Means < c

Translate: “at least c”

Greater than or equal to c

Translate: “at most c”

Less than or equal to c

Translate: “no less than c”

Greater than or equal to c

Translate: “no more than c”

Less than or equal to c

Translate: Ari can harvest at least 48 pounds of honey from her bee colony

The amount of honey Ari can harvest is greater than or equal to 48 pounds

Ari can harvest at least 48 pounds of honey from her bee colony. If she wants to package the honey harvest in 1.5 lbs jars, what’s the minimum number of jars she can fill?

Write an inequality where x represents the number of jars

1.5x is greater than or equal to 48

Ari can harvest at least 48 pounds of honey from her bee colony. If she wants to package the honey harvest in 1.5 lbs jars, what’s the minimum number of jars she can fill?

Write an inequality where x represents the number of jars, and solve

32 jars

Bryan wants to make peppermint stick pickles for his friend (wtf). Each peppermint stick costs $0.40 and each pickle costs $2.30. What’s the greatest number of peppermint stick pickles Bryan can make if he has $20 to buy the ingredient?

Write an inequality where x represents the number of peppermint stick pickles

2.7x is less than or equal to 20

Bryan wants to make peppermint stick pickles for his friend (wtf). Each peppermint stick costs $0.40 and each pickle costs $2.30. What’s the greatest number of peppermint stick pickles Bryan can make if he has $20 to buy the ingredient?

Write an inequality where x represents the number of peppermint stick pickles, and solve

7 pickles

Zoey has $5 and wants to rent a scooter. The scooter costs $1 to unlock, and $0.25 for each minute of use. How many minutes can Zoey ride the scooter for?

Write an inequality where x represents the amount of minutes

1 + 0.25x is less than or equal to 5

Zoey has $5 and wants to rent a scooter. The scooter costs $1 to unlock, and $0.25 for each minute of use. How many minutes can Zoey ride the scooter for?

Write an inequality where x represents the amount of minutes, then solve

16 minutes

A cupcake requires 35 grams of sugar and 50 grams of flour, and a muffin requires 30 grams of sugar and 65 grams of flour. Shawna needs to use up at least 460 grams of sugar and at most 970 grams of flour

Write a system of inequalities where c represents cupcakes and m represents muffins

Sugar: 35c + 30m is greater than or equal to 460

Flour: 50c + 65m is less than or equal to 970

Diego works at a scooter dealership that sells two scooter models: a $5,000 standard model and a $7,000 racing model. Last month, his goal was to sell at least 36 scooters. If Diego met his goal and brought in over $250,000 in sales, which of the following systems of inequalities describes s, the possible number of standard model scooters, and r, the possible number of racing model scooters, that Diego sold last month?

s + r is greater than or equal to 36

5,000s + 7,000r > 250,000

Eugenia wants to buy at least 30 prizes for rewarding her students throughout the semester. The prize pool will be made of small and large prizes, which cost $2 and $5 each respectively. Her budget for the prizes can be no more than $100. She wants to buy at least 15 small prizes and at least 5 large prizes.

Which of the following systems of inequalities represents the conditions described if a is the number of small prizes and y is the number of large prizes?

Small prizes: x is greater than or equal to 15

Large prizes: y is greater than or equal to 5

Total prizes: x + y is greater than or equal to 30

Total money: 2x + 5y is less than or equal to 100

A warehouse worker uses a forklift to move boxes that weigh either 45 pounds or 70 pounds each. Let a be the number of 45-pound boxes and y be the number of 70-pound boxes. The forklift can carry up to either 60 boxes or a weight of 3000 pounds.

Write two equations where one represents the total amount of boxes and the other represents the total weight

Boxes: x + y is less than or equal to 60

Weight: 45x + 70y is less than or equal to 3000

D