Name ______Date ______Core ______
Solving Word Problems with Inequalities
In this lesson we will gain an idea of how the inequalities have meaning in our lives.
Often, people unwittingly use the concept of inequalities in their everyday lives.
1) Carlos goes to the fair where it costs $5 to get in and $0.80 per ride.
a. Write an expression representing the cost of the day after buying x rides.
b. Carlos is allowed to spend at most $25. Write the inequality using the expression you found in part a.
c. Solve the inequality for x. How many rides can he go on?
2) Kristina bought suckers for her children. She gave Linus half of the ones she bought but ended up taking 5 away from him by the end of the day due to poor behavior.
a. Write an expression for the amount of x suckers Linus received.
She gave Nicholas one third of the ones she bought and 3 extra by the end of the day due to good behavior.
b. Write an expression for the amount of x suckers Nicholas received.
Linus had at least as many suckers as Nicholas had at the end of the day.
c. Write an inequality comparing the two expressions you found in part a and b.
d. Solve the inequality for x. What is the minimum number of suckers Kristina bought?
3) Mr. Gleason is opening a new restaurant. He has enough booths to seat up to 40 people. He is ordering tables to fill up the rest of the seating space. Each table can seat up to 6 people.
a. If t represents the number of tables Mr. Gleason orders, write an expression to show the total amount of people that can be seated at booths and tables.
b. Write an inequality that could be used to determine, t, the number of tables Mr. Gleason needs to order so that he has enough seating at booths and tables for at least 125 people. Explain how you found this inequality.
c. Solve the inequality you found in part b.
4) Annah has an assortment of post-it notes in pink, blue, yellow and green. She has 4 times as many blue as pink, three times as many yellow as pink, and twice as many green as pink.
a. Which does she have the least of?
b. Write an expression showing how many blue post-its she has compared to pink.
c. Write an expression showing how many yellow post-its she has compared to pink.
d. Write an expression showing how many green post-its she has compared to pink.
Annah has fewer than 120 post-its.
e. Write an inequality using the expressions you found in parts b – d.
f. Solve the inequality. What is the most number of pink post-it notes she could have?
5) The track team at Hale High School plans to sell t-shirts to raise money for new equipment. At Ted’s Tees, printing costs are $0.80 per shirt and the cost for each T-shirt is $3.75. The shop also charges a $125 fee per order for the silk-screen design.
a. Write an expression showing the costs to make n t-shirts.
b. Write an expression showing the income from selling n t-shirts.
In order for the track team to make a profit, the income from selling the T-shirts must be greater than the cost of making the T-shirts.
c. Write an inequality comparing the two expressions from part a and b.
d. Solve the inequality. How many shirts must they sell to make a profit?
e. The coach has decided that $8.95 is too expensive per shirt. How will lowering the price of the t-shirt affect the number of shirts you have to sell to make a profit?