Question: Lesson 3 Practice Problems
1 This graph describes the relationship between the volume of uncooked rice and the volume
of rice after it is cooked
y (cups of cooked rice)
x (cups of uncooked rice)
a. Write an equation that reflects this relationship where x represents the volume in cups
of uncooked rice and y represents the volume in cups of the rice after it is cooked.
y = 6x
b. Complete the table:
cups of uncooked rice cups of cooked rice
20
120
1
Grade 8 Practice Problems Unit 3
CC BY NC Illustrative
Mathematics, based on IM 6-8
Math, CC BY Open Up Resources
position_hint: center
Graph: A line graph in the center shows a straight line increasing from the origin to about (21, 63), representing y = 3x.
1. **Problem Statement:** We are given a relationship between the volume of uncooked rice $x$ (in cups) and the volume of cooked rice $y$ (in cups). The equation given is $y = 6x$.
2. **Understanding the equation:** This means the volume of cooked rice is 6 times the volume of uncooked rice.
3. **Completing the table:** We use the equation $y = 6x$ to find $y$ for each given $x$.
- For $x = 20$ cups:
$$y = 6 \times 20 = 120$$
- For $x = 120$ cups:
$$y = 6 \times 120 = 720$$
- For $x = 1$ cup:
$$y = 6 \times 1 = 6$$
4. **Final table:**
| Cups of uncooked rice ($x$) | Cups of cooked rice ($y$) |
|-----------------------------|---------------------------|
| 20 | 120 |
| 120 | 720 |
| 1 | 6 |
**Answer:** The equation is $y = 6x$ and the completed table values are $120$, $720$, and $6$ for $x=20$, $120$, and $1$ respectively.