Question

An artist uses 60 pounds of clay to make 80 bowls. The ratio of pounds of clay she uses to the number of bowls she makes is a proportional relationship.

Select all the true statements.

The graph of the proportional relationship has a slope of.

The proportional relationship has a unit rate of a pound of clay per bowl.

She will use 20 pounds of clay to make 15 bowls.

She will use 75 pounds of clay to make 100 bowls.

Answer 1

[AI-generated answer — Bot GPT 3.5]

The graph of the proportional relationship has a slope of 0.75 (60 pounds divided by 80 bowls).

The proportional relationship has a unit rate of 0.75 pounds of clay per bowl.

She will use 20 pounds of clay to make 15 bowls. (This is not true because the unit rate is 0.75 pounds of clay per bowl, so if she makes 15 bowls, she will use 15 x 0.75 = 11.25 pounds of clay.)

She will use 75 pounds of clay to make 100 bowls. (This is not true because the unit rate is 0.75 pounds of clay per bowl, so if she makes 100 bowls, she will use 100 x 0.75 = 75 pounds of clay.)

Answer 2

An artist uses 60 pounds of clay to make 80 bowls. The ratio of pounds of clay she uses to the number of bowls she makes is a proportional relationship.

Select all the true statements.

The graph of the proportional relationship has a slope of 3/4

The proportional relationship has a unit rate of 4/3 a pound of clay per bowl.

She will use 20 pounds of clay to make 15 bowls.

She will use 75 pounds of clay to make 100 bowls.

Answer 3

[AI-generated answer — Bot GPT 3.5]

The graph of the proportional relationship has a slope of 3/4. (This is true because the ratio of pounds of clay to the number of bowls is 60/80, which simplifies to 3/4.)

The proportional relationship has a unit rate of 4/3 a pound of clay per bowl. (This is not true because the unit rate is 3/4 pounds of clay per bowl.)

She will use 20 pounds of clay to make 15 bowls. (This is not true because the unit rate is 3/4 pounds of clay per bowl, so if she makes 15 bowls, she will use 15 x 3/4 = 45/4 pounds of clay.)

She will use 75 pounds of clay to make 100 bowls. (This is not true because the unit rate is 3/4 pounds of clay per bowl, so if she makes 100 bowls, she will use 100 x 3/4 = 75 pounds of clay.)

Answer 4

[AI-generated answer — Explain Bot]

To determine which statements are true, let's analyze the information given:

An artist uses 60 pounds of clay to make 80 bowls. The ratio of pounds of clay she uses to the number of bowls she makes is a proportional relationship.

1. The graph of the proportional relationship has a slope:
In a proportional relationship, the ratio between the two variables remains constant. In this case, the ratio of pounds of clay to the number of bowls is 60:80 or 3:4. The slope of the graph represents this ratio, thus the slope is 3/4.

2. The proportional relationship has a unit rate of a pound of clay per bowl:
In a proportional relationship, the unit rate is determined by the ratio of one unit of the first variable to one unit of the second variable. In this case, the ratio of pounds of clay to the number of bowls is 60:80 or 3:4. The unit rate is 3 pounds of clay per 4 bowls.

3. She will use 20 pounds of clay to make 15 bowls:
To determine if this statement is true, we can set up a proportion. Since the relationship is proportional, we can use the ratio 60:80 to find the answer.

(60 pounds of clay / 80 bowls) = (20 pounds of clay / x bowls)

By cross-multiplying and solving for "x," we get:

60x = 20 * 80
60x = 1600
x = 1600 / 60
x ≈ 26.67

Therefore, she will not use 20 pounds of clay to make 15 bowls.

4. She will use 75 pounds of clay to make 100 bowls:
Similarly, we can set up a proportion to determine if this statement is true:

(60 pounds of clay / 80 bowls) = (75 pounds of clay / 100 bowls)

By cross-multiplying and solving for "75 pounds of clay," we get:

60 * 100 = 80 * 75
6000 = 6000

Therefore, the statement is true. She will use 75 pounds of clay to make 100 bowls.

Based on the analysis, the true statements are:

- The graph of the proportional relationship has a slope of 3/4.
- The proportional relationship has a unit rate of 3 pounds of clay per 4 bowls.
- She will use 75 pounds of clay to make 100 bowls.