General Inequalities and Their Applications

The approach to solving linear inequalities is similar to equations: first, simplify each side, then isolate a variable by doing the same thing to both sides. Remember to switch the sign when multiplying or dividing by a negative number. This lecture series shows examples of solving inequalities and using them to solve word problems. Watch the videos and complete the interactive exercises.

Using inequalities to solve problems - Questions

1. Jacque needs to buy some pizzas for a party at her office. She's ordering from a restaurant that charges a $$7.50$ delivery fee and $$14$ per pizza. She wants to buy as many pizzas as she can, and she also needs to keep the delivery fee plus the cost of the pizzas under $$60$ .

Each pizza is cut into $8$ slices, and she wonders how many total slices she can afford.

Let $P$ represent the number of pizzas that Jacque buys.

1) Which inequality describes this scenario?

Choose 1 answer:

2) What is the largest number of slices that Jacque can afford?

2. Sofia ordered sushi for a company meeting. They change plans and increase how many people will be at the meeting, so they need at least $100$ pieces of sushi in total.

Sofia had already ordered and paid for $24$ pieces of sushi, so she needs to order additional sushi. The sushi comes in rolls, and each roll contains $12$ pieces and costs $$8$ .

Let $R$ represent the number of additional rolls that Sofia orders.

1) Which inequality describes this scenario?

Choose 1 answer:

A. $12+24 R \leq 100$

B. $12+24 R \geq 100$

C. $24+12 R \leq 100$

D. $24+12 R \geq 100$

2) What is the least amount of additional money Sofia can spend to get the sushi they need?

3. Sergei runs a bakery. He needs at least $175$ kilograms of flour in total to complete the holiday orders he's received. He only has $34$ kilograms of flour, so he needs to buy more.

The flour he likes comes in bags that each contain $23$ kilograms of flour. He wants to buy the smallest number of bags as possible and get the amount of flour he needs.

Let $F$ represent the number of bags of flour that Sergei buys.

1) Which inequality describes this scenario?

A. $34+23 F \leq 175$

B. $34+23 F \geq 175$

C. $23+34 F \leq 175$

D. $23+34 F \geq 175$

2) What is the smallest number of bags that Sergei can buy to get the amount of flour he needs?

4. The price of a train ticket consists of an initial fee of $$5$ plus a fee of $$2.75$ per stop. Julia has $$21$ and would like to travel $50$ kilometers. She wants to know the largest number of stops she can afford to buy on a ticket.