# Lesson 17

Modeling with Inequalities

### Problem 1

28 students travel on a field trip. They bring a van that can seat 12 students. Elena and Kiran’s teacher asks other adults to drive cars that seat 3 children each to transport the rest of the students.

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.

### Problem 2

1. In the cafeteria, there is one large 10-seat table and many smaller 4-seat tables. There are enough tables to fit 200 students. Write an inequality whose solution is the possible number of 4-seat tables in the cafeteria.
2. 5 barrels catch rainwater in the schoolyard. Four barrels are the same size, and the fifth barrel holds 10 liters of water. Combined, the 5 barrels can hold at least 200 liters of water. Write an inequality whose solution is the possible size of each of the 4 barrels.
3. How are these two problems similar? How are they different?

### Problem 3

Solve each equation.

1. $$5(n-4)=\text-60$$
2. $$\text-3t+ \text-8=25$$
3. $$7p-8=\text-22$$
4. $$\frac25(j+40)=\text-4$$
5. $$4(w+1)=\text-6$$

### Solution

(From Unit 6, Lesson 9.)

### Problem 4

Select all the inequalities that have the same graph as $$x<4$$.

A:

$$x<2$$

B:

$$x+6<10$$

C:

$$5x<20$$

D:

$$x-2>2$$

E:

$$x<8$$

### Solution

(From Unit 6, Lesson 13.)

### Problem 5

A 200 pound person weighs 33 pounds on the Moon.

1. How much did the person’s weight decrease?

2. By what percentage did the person’s weight decrease?