8.3 Writing Two-Step Inequalities

Three friends earned more than $200 washing cars. They paid their parents $28 for supplies and divided the rest of money equally. Write an inequality to find possible amounts each friend earned. Identify what your variable represents.

• 28a + 3 > 200

• 3a + 28 > 200

• 28 + 3a < 200

• 200 + 3 < 28a

Nick has $7.00. Bagels cost $0.75 each, and a small container of cream cheese costs $1.29. Write an inequality to find the numbers of bagels Nick can buy. Identify what your variable represents.

• 0.75 + 1.29N < 7.00; n = the number of bagels Nick can buy

• 0.75n + 1.29 < 7.00; n = the number of bagels Nick can buy

• 0.75n - 1.29 < 7.00; n = the number cream cheese Nick can buy

• 0.75 - 1.29n > 7.00; n = the number of bagels Nick can buy

Chet needs to buy 4 work shirts, all costing the same amount. The total cost before Chet applies a $25 gift certificate can be no more than $75. Write an inequality to find the possible amounts that Chet pays per shirt. Identify what your variable represents.

• 25a + 4 < 75; a = the maximum amount of the gift card

• 25 + 4a <75; a = the maximum amount each shirt can cost

• 75 + 4a > 25; a = the maximum amount each shirt can cost

• 25a + 4a > 75; a = the maximum amount of the gift card

Due to fire laws, no more than 720 people may attend a performance at Metro Auditorium. The balcony holds 120 people. There are 32 rows on the ground floor, each with the same number of seats. Write an inequality to find the numbers of people that can sit in a ground-floor row if the balcony is full. Identify what your variable represents.

• 120 + 32n < 720; n = the number of people in each row

• 120 + 32n > 720; n = the number of rows

• 720 + 32n < 720; n = the number of people in each row

• 120n + 32n> 720; n = the number of laws

Liz earns a salary of $2,100 per month, plus a commission of 5% of her sales. She wants to earn at least $2,400 this month. Write an inequality to find amounts of sales that will meet her goal. Identify what your variable represents

• 2,100 + 0.05s > 2,400; s = the amount of her sales

• 2,100 + 5s > 2,400; s = the amount of her sales

• 2,100 + 0.05s < 2,400; s = the amount per month

• 2,100s + 0.5 > 2,400; s = the amount of her sales

Lincoln Middle School plans to collect more than 2,000 cans of food in a food drive. So far, 668 cans have been collected. Write an inequality to find numbers of cans the school can collect on each of the final 7 days of the drive to meet this goal. Identify what your variable represents.

• 668 + 7n > 2,000; n = the average number of cans each day

• 2,000 - 7n > 2,000; n = the number of students

• 668 + 7n > 2,000; n = the average number of cans each day

• 2,000 + 7n < 668; n = the number of people donating

Joanna joins a CD club. She pays $7 per month plus $10 for each CD that she orders. Write an inequality to find how many CDs she can purchase in a month if she spends no more than $100. Identify what your variable represents.

• 7c + 10 <100; c = the number of months

• 7 + 10c > 100; c = the number of CDs she buys

• 7c + 100 <10; c = the number of club choices

• 7 + 10c <100; c = the number of CDs she buys

Lionel wants to buy a belt that costs $22. He also wants to buy some shirts that are on sale for $17 each. He has $80. What inequality can you write to find the number of shirts he can buy? Identify what your variable represents.

• 22 + 17n < 80; n = the cost of the belt

• 80 + 17n > 22; n = the cost of the shirts

• 22n + 17 < 80; n = the number of belts he can buy

• 22 + 17n ≤ 80; n = the number of shirts he can buy

Looking at problems 1-8 as examples. Write a real-world problem that can be represented by 15x - 20 ≤ 130.

How would knowing how to write two step equations be useful in your day-to-day life?