Jonah and Aditi make wooden dishes. Jonah makes wooden bowls and Aditi makes wooden plates.

Question

The equation below represents the number of wooden bowls Jonah can make, where x represents the number of hours and y represents the number of wooden bowls. y=4/3x

Aditi can make 5 wooden plates in 4 hours.

Compare the unit rates for Jonah and Aditi to determine which is smaller. Then, plot the ordered pairs that represent the proportional relationship with the smaller unit rate.

Answer 1

To compare the unit rates for Jonah and Aditi, we will first calculate the unit rate for each of them.

Jonah's Unit Rate

The equation for Jonah is given as: \[ y = \frac{4}{3}x \] Where:

• \( y \) is the number of wooden bowls.
• \( x \) is the number of hours.

To find the unit rate of wooden bowls per hour, we can rewrite the equation to isolate the unit rate:

When \( x = 3 \) (to make it easier to calculate): \[ y = \frac{4}{3} \cdot 3 = 4 \] This means Jonah can make 4 bowls in 3 hours.

Calculating the unit rate: \[ \text{Unit rate for Jonah} = \frac{\text{number of bowls}}{\text{number of hours}} = \frac{4 \text{ bowls}}{3 \text{ hours}} \approx 1.33 \text{ bowls/hour} \]

Aditi's Unit Rate

Aditi can make 5 wooden plates in 4 hours. Therefore: \[ \text{Unit rate for Aditi} = \frac{5 \text{ plates}}{4 \text{ hours}} = 1.25 \text{ plates/hour} \]

Comparison

• Jonah's unit rate: \( \approx 1.33 \text{ bowls/hour} \)
• Aditi's unit rate: \( 1.25 \text{ plates/hour} \)

Since \( 1.25 < 1.33 \), Aditi has the smaller unit rate.

Ordered Pairs

To plot the ordered pairs representing the proportional relationship with the smaller unit rate (Aditi's plates), we can use a few different time quantities to build representative points.

Given that Aditi produces 5 plates in 4 hours, we can find additional points:

• For every hour, she makes \( \frac{5 \text{ plates}}{4 \text{ hours}} \) = 1.25 plates/hour.
• In 0 hours, Aditi makes 0 plates.
• In 1 hour, Aditi makes 1.25 plates.
• In 2 hours, Aditi makes \( 2 \times 1.25 = 2.5 \) plates.
• In 3 hours, Aditi makes \( 3 \times 1.25 = 3.75 \) plates.
• In 4 hours, Aditi makes 5 plates.

Ordered pairs for Aditi:

• (0, 0)
• (1, 1.25)
• (2, 2.5)
• (3, 3.75)
• (4, 5)

Summary

Aditi's unit rate is smaller than Jonah's, and the ordered pairs for Aditi that represent her proportional relationship are:

• (0, 0)
• (1, 1.25)
• (2, 2.5)
• (3, 3.75)
• (4, 5)

These would be the points plotted on a graph where the x-axis represents hours and the y-axis represents the number of plates made.