# ﻿Using Equations to Solve Problems

Warmup

Activity #1

Find Corresponding Values in Tables of Proportional Relationships.

In Canadian coins, 16 quarters is equal in value to 2 toonies. • Complete the table and answer the question below.

What does the value next to 1 in the table above mean in this situation?

The following table represents a proportional relationship.

• Fill in the missing parts of the table.

What is the constant of proportionality in the table above?

The following table represents a proportional relationship.

• Fill in the missing parts of the table.

What is the constant of proportionality in the table?

The following table represents a proportional relationship.

• Fill in the missing parts of the table.

Where is the constant of proportionality in the table?

Activity #2

Solve Problems Involving Proportional Relationships.

This is an exercise for you to practice solving problems. Aluminum cans can be recycled instead of being thrown in the garbage. The weight of 10 aluminum cans is 0.16 kilograms. The aluminum in 10 cans that are recycled has a value of \$0.14.

(1.) If a family threw away 2.4 kg of aluminum in a month, how many cans did they throw away? Explain your reasoning.

(2.) What would be the recycled value of those same cans? Explain your reasoning.

(3.) Write an equation to represent the number of cans c  given their weight w .

(4.) Write an equation to represent the recycled value  of  cans.

(5.) Write an equation to represent the recycled value r  of w  kilograms of aluminum.

A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels at this speed in t hours.

(1.) What does the 65 tell us in this situation?

(2.) How many miles does the car travel in 1.5 hours?

(3.) How long does it take the car to travel 26 miles at this speed?

Activity #3

Solve More Problems Involving Proportional Relationships.

This exercise again is for you to demonstrate your problem solving skill. A performer expects to sell 5,000 tickets for an upcoming concert. They want to make a total of \$311,000 in sales from these tickets.

(1.) Assuming that all tickets have the same price, what is the price for one ticket?

(2.) How much will they make if they sell 7,000 tickets?

(3.) How much will they make if they sell 10,000 tickets? 50,000? 120,000? a million? tickets?

(4.) If they make \$404,300, how many tickets have they sold?

(5.) How many tickets will they have to sell to make \$5,000,000?

Aluminum cans can be recycled instead of being thrown in the garbage. The weight of 10 aluminum cans is 0.16 kilograms. The aluminum in 10 cans that are recycled has a value of \$0.14.

(1). What would be the recycled value of those same cans? Explain your reasoning.

(2). Write an equation to represent the number of cans c given their weight w.

(3). Write an equation to represent the recycled value r of c cans.

(4). Write an equation to represent the recycled value r of w kilograms of aluminum.

Challenge #1

Place the decimal point in the appropriate location in the quotient by dragging the point.

Use this answer to find the quotient of the following division problems:

Challenge #2

The EPA estimated that in 2013, the average amount of garbage produced in the United States was 4.4 pounds per person per day. At that rate, how long would it take your family to produce a ton of garbage? (A ton is 2,000 pounds.)

Challenge #3

There are about 1.61 kilometers in 1 mile. Let represent a distance measured in kilometers and represent the same distance measured in miles. Write two equations that relate a distance measured in kilometers and the same distance measured in miles.

Quiz Time