G8

Copyright © Swun Math (^) Grade 8 Unit 4 Lesson 10 P TE

Challenge Problems

Directions: Simplify. Determine the number of solutions.

� 3 �

4

3

푐푐− 2 푑푑�÷(1. 75푐푐 ÷. 875 푐푐)�=

( 20 푐푐− 15 푑푑)

5

Solution:

� 3 �

4

3 푐푐−^2 푑푑

�÷(1. 75푐푐 ÷. 875 푐푐)�=

( 20 푐푐− 15 푑푑)

5

( 4 푐푐− 6 푑푑)÷ 2 = 4푐푐− 3 푑푑

2 푐푐− 3 푑푑= 4푐푐− 3 푑푑

2 푐푐= 4푐푐

In this case, c = 0, but d can have infinite answers.

2. A rectangular prism has a length of 9 , a
   width of 7 , and a height of ℎ. The surface
   area is 126 + 32ℎ. What must be the
   value of ℎ?

Solution:

There are infinite solutions.

Extension Activity

* MP1: Make sense of the problem and persevere in solving it.

* MP4: Apply mathematics in everyday life.

Corrine disagreed with Felicity about the difference between “no solution” and “infinite

solutions.” Corrine said that “no solution” means it was impossible to find an answer

because it was too hard. Felicity said if there’s no solution, there is no answer, and the fact

that there is no solution is the answer itself.

This continued into a difference of opinion about what “infinite solutions” meant. Felicity

says infinite solutions means any number can work, positive or negative; Corrine said that

sometimes it does matter, and infinite solutions might mean only a certain type of number,

positive or negative.

Considering both arguments, who was correct? Why?