Unit 6, Lesson 5
Reasoning about Equations and Tape Diagrams (Part 2)
Grade 7
Practice
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 a total of \$24 for tickets and snacks.
- 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.
\(\displaystyle 6(x+1)=24\)
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.