# Lesson 6

Distinguishing between Two Types of Situations

Let’s think about equations with and without parentheses and the kinds of situations they describe.

### Problem 1

Match each equation to a story. (Two of the stories match the same equation.)

1. $$3(x+5)=17$$
2. $$3x+5=17$$
3. $$5(x+3)=17$$
4. $$5x+3=17$$
1. Jada’s teacher fills a travel bag with 5 copies of a textbook. The weight of the bag and books is 17 pounds. The empty travel bag weighs 3 pounds. How much does each book weigh?
2. A piece of scenery for the school play is in the shape of a 5-foot-long rectangle. The designer decides to increase the length. There will be 3 identical rectangles with a total length of 17 feet. By how much did the designer increase the length of each rectangle?
3. Elena spends $17 and buys a$3 book and a bookmark for each of her 5 cousins. How much does each bookmark cost?
4. Noah packs up bags at the food pantry to deliver to families. He packs 5 bags that weigh a total of 17 pounds. Each bag contains 3 pounds of groceries and a packet of papers with health-related information. How much does each packet of papers weigh?
5. Andre has 3 times as many pencils as Noah and 5 pens. He has 17 pens and pencils all together. How many pencils does Noah have?

### Problem 2

Elena walked 20 minutes more than Lin. Jada walked twice as long as Elena. Jada walked for 90 minutes. The equation $$2(x+20)=90$$ describes this situation. Match each expression with the statement in the story with the expression it represents.

### Problem 3

A school ordered 3 large boxes of board markers. After giving 15 markers to each of 3 teachers, there were 90 markers left. The diagram represents the situation. How many markers were originally in each box?

(From Unit 3, Lesson 2.)

### Problem 4

Select all the pairs of points so that the line between those points has slope $$\frac 2 3$$.

A:

$$(0,0)$$ and $$(2,3)$$

B:

$$(0,0)$$ and $$(3,2)$$

C:

$$(1,5)$$ and $$(4,7)$$

D:

$$(\text-2,\text-2)$$ and $$(4,2)$$

E:

$$(20,30)$$ and $$(\text-20,\text-30)$$

(From Unit 2, Lesson 16.)