# Lesson 4

Reasoning about Equations and Tape Diagrams (Part 1)

### Problem 1

Here are three stories:

• A family buys 6 tickets to a show. They also pay a \$3 parking fee. They spend \$27 to see the show.

• Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself.

• Jada works for 6 hours preparing for the art fair. She spends 3 hours on a sculpture and then paints 27 picture frames.

Here are three equations:

• $$3x+6=27$$
• $$6x+3=27$$
• $$27x+3=6$$
1. Decide which equation represents each story. What does $$x$$ represent in each equation?
2. Find the solution to each equation. Explain or show your reasoning.
3. What does each solution tell you about its situation?

### Problem 2

Here is a diagram and its corresponding equation. Find the solution to the equation and explain your reasoning.

$$6x+11=21$$

### Problem 3

For each object, choose an appropriate scale for a drawing that fits on a regular sheet of paper. Not all of the scales on the list will be used.

Objects

1. A person
2. A football field (120 yards by 53$$\frac{1}{3}$$ yards)
3. The state of Washington (about 240 miles by 360 miles)
4. The floor plan of a house
5. A rectangular farm (6 miles by 2 mile)

Scales

• 1 in : 1 ft
• 1 cm : 1 m
• 1: 1000
• 1 ft: 1 mile
• 1: 100,000
• 1 mm: 1 km
• 1: 10,000,000

### Solution

(From Unit 2, Lesson 7.)

### Problem 4

The diagram shows two intersecting lines.

Find the missing angle measures.