Lesson 5
Reasoning about Equations and Tape Diagrams (Part 2)
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
Solution
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(From Unit 4, Lesson 2.)Problem 2
Find the products.
- \(\frac23 \boldcdot \left(\frac {\text{-}4}{5}\right)\)
- \(\left(\frac {\text{-}5}{7}\right) \boldcdot \left(\frac {\text7}{5}\right)\)
- \(\left(\frac {\text{-}2}{39}\right) \boldcdot 39\)
- \(\left(\frac {\text2}{5}\right) \boldcdot \left(\frac {\text{-}3}{4}\right)\)
Solution
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(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:
- \(3(x+6)=24\)
- \(6(x+3)=24\)
- 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?
Solution
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Problem 4
Here is a diagram and its corresponding equation. Find the solution to the equation and explain your reasoning.
![Tape diagram, 6 equal parts labeled x + 1, total 24](https://cms-im.s3.amazonaws.com/d1W7yL8nt8LAtuMo9scB2t91?response-content-disposition=inline%3B%20filename%3D%227-7.6.A5.newPP.01.png%22%3B%20filename%2A%3DUTF-8%27%277-7.6.A5.newPP.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T172648Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=110f088b3ebcd00405b76478cd69667958069e46e5be9878d1b8a9aa6087df61)
\(\displaystyle 6(x+1)=24\)
Solution
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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?
\(9^\circ \text{C}, \text-3^\circ \text{C}, 22^\circ \text{C}, \text-5^\circ \text{C}, 11^\circ \text{C}, 15^\circ \text{C}\)
Solution
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(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.
Solution
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(From Unit 4, Lesson 11.)