# Using Equations to Solve Problems

Warmup

Without calculating, drag these expressions to order their quotients from least to greatest.

Activity #1

`Balance a Scale.`

The scale you see below was loaded with a certain number of red packets on the left tray. • Try to balance the scale by loading blue packets on the right scale using the blue slider to increase their number. ​
• Once you find out how many blue packets you need, you may request a new challenge by clicking the button in the upper left corner.

Activity #2

` Use Scale Diagram to Solve Real World Problems.`

Tyler is making invitations to the fair. He has already made some of the invitations, and he wants to finish the rest of them within a week. He is trying to spread out the remaining work, to make the same number of invitations each day.
Tyler draws a diagram to represent the situation. • Study the scale diagram below and answer the questions.

(1.) Explain how each part of the situation is represented in Tyler’s diagram:

(2.) How many total invitations Tyler is trying to make.

(4.) How many days he has to finish the invitations.

(5.) How many invitations should Tyler make each day to finish his goal within a week? Explain or show your reasoning.

(6.) Use Tyler’s diagram to write an equation that represents the situation.

(7.) Explain how each part of the situation is represented in your equation.

(8.) Explain or show how to solve your equation.

Activity #3

` Solve Exercise Problems.` Priya, Han, and Elena, are members of the running club at school. Priya was busy studying this week and ran 7 fewer miles than last week. She ran 9 times as far as Elena ran this week. Elena only had time to run 4 miles this week.

(1.) How many miles did Priya run last week?

(2.) Elena wrote the equation to describe the situation. She solved the equation by multiplying each side by 9 and then adding 7 to each side.

(3.) How does Elena’s solution compare to the way you found Priya’s miles?

(4.) One day last week, 6 teachers joined of the members of the running club in an after-school run. Priya counted a total of 31 people running that day. How many members does the running club have?

(5.) Priya and Han plan a fundraiser for the running club. They begin with a balance of -80 because of expenses. In the first hour of the fundraiser they collect equal donations from 9 family members, which brings their balance to -44. How much did each parent give?

(6.) The running club uses the money they raised to pay for a trip to a canyon. At one point during a run in the canyon, the students are at an elevation of 128 feet. After descending at a rate of 50 feet per minute, they reach an elevation of -472 feet. How long did the descent take?

Challenge #1

The baby giraffe weighed 132 pounds at birth. He gained weight at a steady rate for the first 7 months until his weight reached 538 pounds.

Challenge #2

Find the value of each variable below.

Challenge #3

Match each equation to its solution and to the story it describes.

Quiz Time