Lesson 5: Practice Problems

Problem 1 From Unit 4 Lesson 2

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 $\frac{1}{2}$ pound of cheese
$8.25 for $1 \frac{1}{2}$ pounds of coffee beans
$6.75 for $\frac{3}{4}$ pounds of fudge
$5.50 for a $6 \frac{1}{4}$ pound pumpkin

Problem 2 From Unit 5 Lesson 9

Find the products.

$\frac{2}{3} \cdot (\frac{- 4}{5})$
$(\frac{- 5}{7}) \cdot (\frac{7}{5})$
$(\frac{- 2}{39}) \cdot 39$
$(\frac{2}{5}) \cdot (\frac{- 3}{4})$

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.

A tape diagram labeled 24 with 6 segments labeled "x+1"

$6 (x + 1) = 24$

Problem 5 From Unit 5 Lesson 7

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?

$9^{\circ} C, - 3^{\circ} C, 22^{\circ} C, - 5^{\circ} C, 11^{\circ} C, 15^{\circ} C$

Problem 6 From Unit 4 Lesson 11

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.