A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts.

Question

Which points did the group leader label?



Responses

(0, 8) and (16, 0)
Begin ordered pair 0 comma 8 end ordered pair and Begin ordered pair 16 comma 0 end ordered pair

(0, 16) and (8, 0)
Begin ordered pair 0 comma 16 end ordered pair and Begin ordered pair 8 comma 0 end ordered pair

(0, 30) and (15, 0)

Begin ordered pair 0 comma 30 end ordered pair and Begin ordered pair 15 comma 0 end ordered pair

(0, 15) and (30, 0)

Answer 1

To determine the intercepts, we can set up the following equation for the total amount of spaghetti sauce using small jars (8 oz) and large jars (16 oz):

Let:

• \( x \) = number of small jars
• \( y \) = number of large jars

The equation representing the total amount of sauce is:

\[ 8x + 16y = 240 \]

To find the intercepts:

1. Find the x-intercept: Set \( y = 0 \):

\[ 8x + 16(0) = 240 \ 8x = 240 \ x = \frac{240}{8} = 30 \]

So, the x-intercept is \( (30, 0) \).

2. Find the y-intercept: Set \( x = 0 \):

\[ 8(0) + 16y = 240 \ 16y = 240 \ y = \frac{240}{16} = 15 \]

So, the y-intercept is \( (0, 15) \).

The intercepts labeled by the group leader are \( (0, 15) \) and \( (30, 0) \).

Therefore, the correct response is:

(0, 15) and (30, 0).