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Linear inequalities (two variables)

Total questions: 20

Worksheet time: 15mins

Name
Class
Date
1.

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?

a)

2x + 3y ≥\ge 100

x + y ≤\le 40

b)

100x + 2y ≥\ge 3

x + y ≤\le 40

c)

100x + 40y ≥\ge 100

3x + 2y ≤\le 40

d)

3x + 2y ≥\ge 100

x + y ≤\le 40

2.

The automotive plant in Compton makes the White Vans and the Bugatti's. The plant has a maximum production capacity of 1200 cars per week. During the spring, a dealer orders up to 600 White Vans and 800 Bugatti's each week. What the inequality to represent the situation? (X equals White Vans and Y equals Bugatti's

a)

x+y≤1,200

b)

x-y=1,200

c)

x+y<1,200

d)

x+y=1,200

3.

Jon is buying flowers for his wife. Roses are $3 each, and tulips cost $2 each.

Let x = number of roses

Let y = number of tulips


Jon has a budget of $50. Which inequality models this scenario?

a)

3x + 2y ≤\le 50

b)

3x + 2y < 50

c)

3x + 2y > 50

d)

3x + 2y ≥\ge 50

4.

Cole is doing a basketball challenge for charity. In order to win money for the charity, he needs to score at least 20 points in less than 10 shots. If x is the number of 2-point shots, and y is the number of three point shots, which inequalities below represent the situation?

a)

x+y<10x+y<10

2x+3y≥202x+3y\ge20

b)

x+y≤10x+y\le10
2x+3y≥202x+3y\ge20

c)

x+y≤10x+y\le10
2x+3y>202x+3y>20

d)

x+y<10x+y<10
2x+3y>202x+3y>20

5.
It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?
a)
2x + 3y ≤ 18
b)
x + y ≤ 6
c)
x + y ≤ 9
d)
3x + 2y ≤ 18
6.

You need to earn at least $85 to cover your gas and food expenses. Your babysitting job pays $7.50 per hour and your math tutoring job pays $6 per hour. Write an inequality that represents this situation.

a)

 7.5b+6m>857.5b+6m>85  

b)

 7.5b+6m<857.5b+6m<85  

c)

 7.5b+6m≥857.5b+6m\ge85  

d)

 7.5b+6m≤857.5b+6m\le85  

7.

Which inequality represents this situation?


Sania is playing a phone game in which she pops balloons and slices fruit. She earns 7 points for popping balloons and 12 points for slicing fruit. She needs to score at least 650 points.

a)

 7B+13F≤6507B+13F\le650 

b)

 7B+13F≥6507B+13F\ge650 

c)

 7B+13F<6507B+13F<650 

d)

 7B+13F>6507B+13F>650 

8.

Michael is selling chocolate bars and orange juice in a carnival. Chocolate bars sell for 2.50 each, and orange juice sell for 3.50 each. If Michael wants to get more than 150, write an inequality showing the number of chocolate bars, b, and the number of orange juice, j, he must sell.

a)

2.50b + 3.50m > 150

b)

2.50b + 3.50m <150

c)

2.50m + 3.50b > 150

d)

2.50m + 3.50b <1

9.

A factory produces p handphones of model X and r handphones of model Y. The number of handphones of model Y cannot exceed the number of handphones of model X by more than 150. Which linear inequality represents the situation?

a)

p−r≥150p-r\ge150

b)

p−r<150p-r<150

c)

r−p<150r-p<150

d)

r−p≤150r-p\le150

10.

A charity organization wants to distribute food packages and blankets to a disaster-stricken area. They can buy a food package, x, for $20 and a blanket, y, for $15. They have a budget of $5000.

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

a)

20x+15y>500020x+15y>5000

b)

20x+15y<500020x+15y<5000

c)

20+x+15+y>500020+x+15+y>5000

d)

20+x+15+y<500020+x+15+y<5000

11.

Student Council is selling wrapping paper p and cheescakes c for a fundraiser. The wrapping paper costs $5 per roll and the cheesecakes cost $15 each. Student Council wants to exceed $2000 in sales. Which inequality expresses the constraint for sales?

a)

p + c > 2000

b)

5p + 15s > 2000

c)

p + s < 2000

d)

5p + 15s < 2000

12.
Write the linear inequality in standard form for this situation: The CRHS science department can spend no more than $2700 on textbooks this year. The department needs to buy both Biology text books, which cost $57 each, and Chemistry textbooks, which cost $72 each.
a)
57x + 72y ≥ 2700
b)
57x + 72y > 2700
c)
57x + 72y < 2700
d)
57x + 72y ≤ 2700
13.

Write the linear inequality in standard form for this situation:

Ms. Johnson is ordering pizzas and breadsticks for a school party and has a budget of no more than $81.

An order of breadsticks costs $7 and a pizza costs $13.

a)

7x + 13y < 81

b)

7x + 13y ≥ 81

c)

7x + 13y ≤ 81

d)

7x + 13y > 81

14.

Molly is sewing some clothing. She has 66 yards of fabric to use. She uses 4 yards of fabric to make a short-sleeved shirt, x, and 16 yards of fabric to make a long-sleeved shirt, y.

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

a)

b)

c)

d)

15.

Jessi is raising money for her society club. T-shirt sell for RM10 each, and DIY accessories organizer sell for RM15 each. If Jessi wants to raise more than RM1500, write an inequality showing the number of T-shirt, t, and the number of ,a, she must sell.

a)

10t + 15a > 1500

b)

10t + 15a < 1500

c)

10t + 15a ≥ 1500

d)

10t + 15a ≤ 1500

16.

The number of apples (a) more than twice the number of ponkans (p) is greater than 24.

a)

2p + a > 24

b)

2p + a < 24

c)

2p - a > 24

d)

2p + a ≥ 24

17.

2.)   During a sale, all headphones cost $26 and all cell phone cases cost $14. Derrick is buying these products as gifts for his friends plans to spend at least $150.

a) Inequality: ___________________

a)

26x+14y≤15026x+14y\le150

b)

14x−26y<15014x-26y<150

c)

150x+14y≥26150x+14y\ge26

d)

26x+14y≥15026x+14y\ge150

18.

For a school play, adults tickets a cost $12 and student tickets s cost $8. The drama club wants to collect at least $5000. Which inequality expresses the constraint on income?

a)

12a + 8s < 5000

b)

12a + 8s > 5000

c)

12a + 8s < 5000

d)

12a + 8s > 5000

19.

In order to raise money to attend upcoming competitions, the debate team at Lancaster High School is selling apple cider and hot chocolate at a basketball game. They hope to make at least $170 in revenue at tonight's game, with hot chocolate, x, selling for $1 and hot apple cider, y, selling for $2.

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

a)

b)

c)

d)

20.

A grill at a barbecue restaurant will be used to cook sausage links that are 2 lb each and briskets that are 6 lb each. No more than 120 lb of sausage links and briskets will be cooked on the grill.

Which inequality represents all possible combinations of x, the number of sausage links that will be cooked on the grill, and y, the number of briskets that will also be cooked?

a)

6x+2y<1206x+2y<120  

b)

2x+6y≤1202x+6y\le120  

c)

6x+2y>1206x+2y>120  

d)

2x+6y≥1202x+6y\ge120