SYSTEMS OF EQUATIONS AND INEQUALITIES WORKSHEET

Problem 1 :

Only chocolate and vanilla ice cream cones are sold at an ice cream store. In one day, the number of chocolate cones are sold was 1 more than 4 times the number of Vanilla cones sold. A total of 121 cones were sold that day. 

• Write equations to determine the number of chocolate cones sold that day.
• Use equations to determine the number of chocolate cones sold that day.

Solution

Problem 2 :

The math club sells candy bars and drinks during foot ball games.

• 60 candy bars and 110 drinks will sell for $265
• 120 candy bars and 90 drinks will sell for $270

How much does each candy bar sell for ?

Solution

Problem 3 :

Two times Antonio's age plus three times Sarah's age equals 34. Sarah's age is also five times Antonio's age. How old is Sarah ?

Solution

Problem 4 :

Paul sells chocolate chip cookies and peanut butter cookies. 

• Baking a batch of chocolate chip cookies takes 1.75 cups of flour and 2 eggs.
• Baking a batch of peanut chip cookies takes 1.25 cups of flour and 1 egg.
• Paul has 10 cups of flour and 12 eggs.
• He makes $4 profit per batch and chocolate chip cookies.
• He makes $2 profit per batch and peanut butter cookies.

How many batches of peanut butter cookies should Paul make to maximize his profit ?

a)  1     b)  2     c)   5    d)  8

Solution

Problem 5 :

Which ordered pair is in the solution set of the system of inequalities shown in the graph given below.

a)  (-2, -1)     b)  (-2, -4)     c)   (-2, 2)    d)  (2, -2)

Solution

Problem 6 :

Which is the graph of the solution of the system of inequalities ?

x - 2y ≤ 10

2x + y > 0

Solution

Problem 7 :

Lucy and Barbara began saving money the same week.  The table below shows the models for the amount of money Lucy and Barbara had saved after x weeks.

After how many weeks will Lucy and Barbara have the same amount of money saved ?

a)  1.1 weeks      b)  1.7 weeks     c)   8 weeks    d)  12 weeks

Solution

Problem 8 :

Which ordered pair is not in the solution set of 

y > 2x + 1

a)  (1, 4)     b)  (1, 6)    c)   (3, 8)    d)  (2, 5)

Solution

Problem 9 :

What scenario could be modeled by the graph below ?

a)  The number of pounds of apples, y,  minus two times the number of pounds of oranges x, is at most 5.

b)  The number of pounds of apples, y minus half the number of pounds of oranges x, is at most 5.

c)  The number of pounds of apples, y plus two times the number of pounds of oranges x, is at most 5.

d)  The number of pounds of apples, y plus half the number of pounds of oranges x, is at most 5.

Solution

Problem 10 :

James is at a gift sale where everything costs $4 (included tax)

• James has $50
• James has atleast 28 remaining when he is finished buying gifts 

What is the greatest number of gifts he can buy ?

Solution