SOLVING LINEAR INEQUALITIES WORD PROBLEMS IN TWO VARIABLES

Problem 1 :

Katie has $50 in a savings account at the beginning of the summer. She wants to have at least $20 in the account by the end of the summer. She withdraws $2 each week for food, clothes, and movie tickets. Write an inequality that expresses Katie’s situation and display it on the graph below. For how many weeks can Katie withdraw money?

Solution :

Let x be the number of weeks 

50 - 2x ≥ 20

2x ≤ 30

x ≤ 15 weeks

Problem 2 :

Skate Land charges a $50 flat fee for a birthday party rental and $4 for each person. Joann has no more than $100 to budget for her party. Write an inequality that models her situation and display it on the graph below. How many people can attend Joann's party.

Solution :

Assume x people can attend the party.

y = 50 + 4x

y ≤ 100

50 + 4x ≤ 100

4x ≤ 50

x ≤ 12.5

So, 12 people can attend Joan’s party.

Problem 3 :

Sarah is selling bracelets and earrings to make money for summer vacation. The bracelets cost $2 and the earrings cost $3. She needs to make at least $60. Sarah knows she will sell more than 10 bracelets. Write inequalities to represent the income from jewelry sold and number of bracelets sold. Find two possible solutions.

Solution :

Let x be the number of bracelets sold.

Let y be the number of earrings sold.

2x + 3y ≥ 60

x > 10

If x = 11, then 2(11) + 3y ≥ 60

3y ≥ 60 - 22

3y ≥ 38

Since y is the number of earrings, x = 11 is not possible.