# 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.

1. $5 for 4 pounds of apples 2.$3.50 for $$\frac12$$ pound of cheese
3. $8.25 for $$1\frac12$$ pounds of coffee beans 4.$6.75 for $$\frac34$$ pounds of fudge
5. $5.50 for a $$6\frac14$$ pound pumpkin (From Unit 4, Lesson 2.) ### Problem 2 Find the products. 1. $$\frac23 \boldcdot \left(\frac {\text{-}4}{5}\right)$$ 2. $$\left(\frac {\text{-}5}{7}\right) \boldcdot \left(\frac {\text7}{5}\right)$$ 3. $$\left(\frac {\text{-}2}{39}\right) \boldcdot 39$$ 4. $$\left(\frac {\text2}{5}\right) \boldcdot \left(\frac {\text{-}3}{4}\right)$$ (From Unit 5, Lesson 9.) ### 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: • $$3(x+6)=24$$ • $$6(x+3)=24$$ 1. Which equation represents which story? 2. What does $$x$$ represent in each equation? 3. Find the solution to each equation. Explain or show your reasoning. 4. 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? $$9^\circ \text{C}, \text-3^\circ \text{C}, 22^\circ \text{C}, \text-5^\circ \text{C}, 11^\circ \text{C}, 15^\circ \text{C}$$ (From Unit 5, Lesson 7.) ### 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.

(From Unit 4, Lesson 11.)