# Lesson 5

Reasoning about Equations and Tape Diagrams (Part 2)

Let’s use tape diagrams to help answer questions about situations where the equation has parentheses.

### Problem 1

Here are some prices customers paid for different items at a farmer’s market. Find the cost for 1 pound of each item.

- $5 for 4 pounds of apples
- $3.50 for \(\frac12\) pound of cheese
- $8.25 for \(1\frac12\) pounds of coffee beans
- $6.75 for \(\frac34\) pounds of fudge
- $5.50 for a \(6\frac14\) pound pumpkin

### Problem 2

Find the products.

- \(\frac23 \boldcdot \left(\frac {\text{-}4}{5}\right)\)
- \(\left(\frac {\text{-}5}{7}\right) \boldcdot \left(\frac {\text7}{5}\right)\)
- \(\left(\frac {\text{-}2}{39}\right) \boldcdot 39\)
- \(\left(\frac {\text2}{5}\right) \boldcdot \left(\frac {\text{-}3}{4}\right)\)

### Problem 3

Here are two stories:

- A family buys 6 tickets to a show. They also
*each*spend $3 on a snack. They spend $24 on the show.

- Diego has 24 ounces of juice. He pours equal amounts for each of his 3 friends, and then adds 6 more ounces for each.

Here are two equations:

- \(3(x+6)=24\)
- \(6(x+3)=24\)

- Which equation represents which story?
- What does \(x\) represent in each equation?
- Find the solution to each equation. Explain or show your reasoning.
- What does each solution tell you about its situation?

### Problem 4

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

\(\displaystyle 6(x+1)=24\)

### Problem 5

Below is a set of data about temperatures. The *range* of a set of data is the distance between the lowest and highest value in the set. What is the range of these temperatures?

\(9^\circ \text{C}, \text-3^\circ \text{C}, 22^\circ \text{C}, \text-5^\circ \text{C}, 11^\circ \text{C}, 15^\circ \text{C}\)

### Problem 6

A store is having a 25% off sale on all shirts. Show two different ways to calculate the sale price for a shirt that normally costs $24.