Question
With 15 pounds of tomatoes, Just Juice Company can produce 9 pints of tomato juice. Which of the
following correctly represent this proportional relationship?
Select all that apply.
햠 j 5 0.6 t, where j 5 the number of pints of juice and t 5 the number of pounds of tomatoes
햡
Tomato Juice (pints)
5 15 25 30
Tomatoes (pounds)
3 9 15 18
햢
y
x
0 1 2 3 4 5 6 7 8 9 10
Tomatoes (pounds)
T
o
m
a
t
o
J
u
i
c
e
(
p
i
n
t
s
)
10
8
6
4
2
(5, 3)
(10, 6)
햣
Tomato Juice (pints)
6 12 18 24
Tomatoes (pounds)
10 20 30 40
햤 j 5 1
2
}
3
t, where j 5 the number of pints of juice and t 5 the number of pounds of tomatoes
following correctly represent this proportional relationship?
Select all that apply.
햠 j 5 0.6 t, where j 5 the number of pints of juice and t 5 the number of pounds of tomatoes
햡
Tomato Juice (pints)
5 15 25 30
Tomatoes (pounds)
3 9 15 18
햢
y
x
0 1 2 3 4 5 6 7 8 9 10
Tomatoes (pounds)
T
o
m
a
t
o
J
u
i
c
e
(
p
i
n
t
s
)
10
8
6
4
2
(5, 3)
(10, 6)
햣
Tomato Juice (pints)
6 12 18 24
Tomatoes (pounds)
10 20 30 40
햤 j 5 1
2
}
3
t, where j 5 the number of pints of juice and t 5 the number of pounds of tomatoes
Answers
GPT-4o mini
To determine which of the given options correctly represent the proportional relationship between the number of pints of tomato juice (j) and the number of pounds of tomatoes (t) that Just Juice Company can produce, we first need to establish the ratio from the information given:
- 15 pounds of tomatoes produces 9 pints of tomato juice.
We can find the ratio by dividing the number of pints by the number of pounds:
\[
\frac{j}{t} = \frac{9}{15} = \frac{3}{5}
\]
This means that for every 5 pounds of tomatoes, 3 pints of tomato juice can be produced. Therefore, we can express this relationship in various forms.
Let's evaluate the options provided:
### Option 1: \( j = 0.6t \)
To check if this equation represents the ratio \( \frac{3}{5} \):
- The ratio \( 0.6 \) is equivalent to \( \frac{6}{10} \) which simplifies to \( \frac{3}{5} \).
- **This option is correct.**
### Option 2:
- **Tomato Juice (pints):** 5, 15, 25, 30
- **Tomatoes (pounds):** 3, 9, 15, 18
To check if this set of values reflects the established ratio:
- For 3 pounds of tomatoes, \( 3 \text{ pounds} \rightarrow 5 \text{ pints} \) gives \( \frac{5}{3} \) (not equal to \( \frac{3}{5} \)).
- For 9 pounds of tomatoes, \( 9 \text{ pounds} \rightarrow 15 \text{ pints} \) gives \( \frac{15}{9} = \frac{5}{3} \) (not equal to \( \frac{3}{5} \)).
- This set does not follow the established ratio.
- **This option is not correct.**
### Option 3:
- **Tomatoes (pounds):** 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- **Tomato Juice (pints):** 10, 8, 6, 4, 2
We can derive the values here and see if they represent the ratio:
- The ratio is not consistent — as the number of pounds increases, the number of pints decreases. This does not follow a proportional relationship as described.
- **This option is not correct.**
### Option 4: \( j = \frac{1}{2} \cdot \frac{3}{t} \)
This version seems to mix up the calculations:
If we try \( j = \frac{1}{2} \cdot \frac{3}{t} \), it does not give a clear linear relationship and the constant proportions are incorrect.
- **This option is not correct.**
### Conclusion:
The only correct option that accurately reflects the proportional relationship is:
- \( j = 0.6t \) (Option 1).
So, the answer is **only Option 1 is correct.**
- 15 pounds of tomatoes produces 9 pints of tomato juice.
We can find the ratio by dividing the number of pints by the number of pounds:
\[
\frac{j}{t} = \frac{9}{15} = \frac{3}{5}
\]
This means that for every 5 pounds of tomatoes, 3 pints of tomato juice can be produced. Therefore, we can express this relationship in various forms.
Let's evaluate the options provided:
### Option 1: \( j = 0.6t \)
To check if this equation represents the ratio \( \frac{3}{5} \):
- The ratio \( 0.6 \) is equivalent to \( \frac{6}{10} \) which simplifies to \( \frac{3}{5} \).
- **This option is correct.**
### Option 2:
- **Tomato Juice (pints):** 5, 15, 25, 30
- **Tomatoes (pounds):** 3, 9, 15, 18
To check if this set of values reflects the established ratio:
- For 3 pounds of tomatoes, \( 3 \text{ pounds} \rightarrow 5 \text{ pints} \) gives \( \frac{5}{3} \) (not equal to \( \frac{3}{5} \)).
- For 9 pounds of tomatoes, \( 9 \text{ pounds} \rightarrow 15 \text{ pints} \) gives \( \frac{15}{9} = \frac{5}{3} \) (not equal to \( \frac{3}{5} \)).
- This set does not follow the established ratio.
- **This option is not correct.**
### Option 3:
- **Tomatoes (pounds):** 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- **Tomato Juice (pints):** 10, 8, 6, 4, 2
We can derive the values here and see if they represent the ratio:
- The ratio is not consistent — as the number of pounds increases, the number of pints decreases. This does not follow a proportional relationship as described.
- **This option is not correct.**
### Option 4: \( j = \frac{1}{2} \cdot \frac{3}{t} \)
This version seems to mix up the calculations:
If we try \( j = \frac{1}{2} \cdot \frac{3}{t} \), it does not give a clear linear relationship and the constant proportions are incorrect.
- **This option is not correct.**
### Conclusion:
The only correct option that accurately reflects the proportional relationship is:
- \( j = 0.6t \) (Option 1).
So, the answer is **only Option 1 is correct.**