Lesson 3

Comparing Proportional Relationships

Let’s compare proportional relationships.

Problem 1

A contractor must haul a large amount of dirt to a work site. She collected information from two hauling companies.

EZ Excavation gives its prices in a table.

dirt
(cubic yards)		 cost
(dollars)
8 196
20 490
26 637

Happy Hauling Service gives its prices in a graph.

graph, horizontal axis, dirt in cubic yards, scale 0 to 6, by 1's. vertical axis, cost in dollars, scale 0 to 55, by 5's. line passing through origin, 1 comma 25 and 2 comma 50.
  1. How much would each hauling company charge to haul 40 cubic yards of dirt? Explain or show your reasoning.
  2. Calculate the rate of change for each relationship. What do they mean for each company?
  3. If the contractor has 40 cubic yards of dirt to haul and a budget of $1000, which hauling company should she hire? Explain or show your reasoning.
     

Problem 2

Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation \(y=118x\), where \(y\) is the number of steps and \(x\) is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walk for a total of 5 hours. Who walks more steps? How many more?

Problem 3

Find the coordinates of point \(D\) in each diagram:

xy plane with no grid. right triangle with vertices at -6 comma 0, 2 comma 10, and 2 comma 0. hypotenuse crosses y axis at D. 
xy plane with no grid. right triangle with vertices at -4 comma 3, 2 comma 7, and 2 comma 3. hypotenuse crosses y axis at D. 
(From Unit 2, Lesson 16.)

Problem 4

Solve each equation.

\(\frac17a+\frac34=\frac98\)

\(\frac23+\frac15b=\frac56\)

\(\frac32=\frac43c+\frac23\)

\(0.3d+7.9=9.1\)

\(11.03=8.78+0.02e\)

(From Unit 3, Lesson 7.)