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.](https://staging-cms-im.s3.amazonaws.com/2RkK2SGArYJgYNgMezguwLY8?response-content-disposition=inline%3B%20filename%3D%228-8.3.A3.dirtgraph.2.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.A3.dirtgraph.2.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143344Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e16b5fa286aa1306aab79c499e6bb4d6e1f2ec7e447ef88eed32bd8259d7c329)
- How much would each hauling company charge to haul 40 cubic yards of dirt? Explain or show your reasoning.
- Calculate the rate of change for each relationship. What do they mean for each company?
- 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.](https://staging-cms-im.s3.amazonaws.com/8iQvRy5dXTDE6jDYAeTiQDGA?response-content-disposition=inline%3B%20filename%3D%228-8.2.C.PP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C.PP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143344Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=30f29a870ef80896b5e51fd2d2146457c7c34b51a21a017dc5722edbcb163231)
![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.](https://staging-cms-im.s3.amazonaws.com/HW84Na6KqSj8MyRE25zRQoAR?response-content-disposition=inline%3B%20filename%3D%228-8.2.C.PP.Image.01.1.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.C.PP.Image.01.1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143344Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5ffa3cd2d01c6540415dd36189b6d518795764d8f7a00ab82e75ea2ca6666a27)
Problem 4
Solve each equation.
\(\frac17a+\frac34=\frac98\)
\(\frac23+\frac15b=\frac56\)
\(\frac32=\frac43c+\frac23\)
\(0.3d+7.9=9.1\)
\(11.03=8.78+0.02e\)