Lesson 5: Practice Problems

Problem 1

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 2

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 3 From Unit 2 Lesson 11

Find a sequence of rotations, reflections, translations, and dilations showing that one figure is similar to the other. Be specific: give the amount and direction of a translation, a line of reflection, the center and angle of a rotation, and the center and scale factor of a dilation.

A circular grid with center point A and two figures - B'C'D'E' and a second larger figure BCDE

Problem 4

Suppose Quadrilaterals $A$ and $B$ are both squares. Are $A$ and $B$ necessarily scale copies of one another? Explain.