Lesson 5

Reasoning about Equations and Tape Diagrams (Part 2)

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:

• $$3(x+6)=24$$
• $$6(x+3)=24$$
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 2

Here is a diagram and its corresponding equation. Find the solution to the equation and explain your reasoning.

$$\displaystyle 6(x+1)=24$$

Problem 3

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.