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.

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)

1 answer

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=2408=30

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

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

8(0)+16y=240 16y=240 y=24016=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).