Unit 6, Lesson 17
Modeling with Inequalities
Grade 7
Practice
Problem 1
There are 28 students going on a field trip. The school has a van that can seat 12 students. The rest of the students will ride in cars, with 3 students in each car.
Elena wonders if she should use the inequality \(12+3n>28\) or \(12+3n\geq28\) to figure out how many cars are needed. Kiran doesn’t think it matters in this case. Do you agree with Kiran? Explain your reasoning.
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Problem 2
- A school principal is ordering tables for the cafeteria. There is already one large, 10-seat table that they are keeping. All the new tables will have 4 seats. The cafeteria needs to seat at least 200 students. Write an inequality whose solution is the number of 4-seat tables the principal should order.
- The principal is also ordering rain barrels to collect water in the schoolyard. The school already has one small barrel that holds 10 gallons. The principal wants to order 4 more barrels so that all the barrels combined will hold at least 200 gallons. Write an inequality whose solution is the size of each of the 4 barrels if they are the same size.
- How are these two problems similar? How are they different?
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Problem 3
Solve each equation.
\(5(n-4)=\text-60\)
\(\text-3t+ \text-8=25\)
\(7p-8=\text-22\)
\(\frac25(j+40)=\text-4\)
\(4(w+1)=\text-6\)
Problem 4
Select all the inequalities for which the solution matches this number line.
\(x<2\)
\(x+6<10\)
A lunar rover that weighs 200 pounds on Earth will weigh 33 pounds on the Moon.
- How much does the rover’s weight decrease?
- By what percentage does the rover’s weight decrease?
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