Question

The pumpkin patch sells medium pumpkins for $6 and large pumpkins for $9. Jillian goes to the pumpkin path with $36. Write an equation in standard form that represents the number of medium and large pumpkins Jillian can buy. How many medium pumpkins can Jillian buy if she does not buy any large pumpkins? How would this be represented on a graph, what is the point called?

Answer 1

Jillian can represent the number of pumpkins she can buy with the equation 6m + 9l = 36. If she doesn't buy large pumpkins, she can buy 6 medium pumpkins. This is represented by the point (0, 6) on a graph, known as the intercept.

Step-by-step explanation:

To represent the number of medium and large pumpkins Jillian can buy, let m be the number of medium pumpkins and l be the number of large pumpkins. The cost of medium pumpkins is $6 each, and the cost of large pumpkins is $9 each. Jillian has $36 to spend, so the equation in standard form would be:

6m + 9l = 36

If Jillian does not buy any large pumpkins, then l is 0. The equation simplifies to 6m = 36, which means Jillian can buy 6 medium pumpkins, as m = 6.

On a graph, this scenario would be represented by a point on the horizontal axis (where l=0) at the coordinate (0, 6). This point represents the maximum number of medium pumpunks Jillian can afford without purchasing any large pumpkins and is often referred to as the intercept.