Answer:
To find out how many yogurt sundaes and cones Ryleigh can buy, we need to solve the inequality 4x + 3y ≤ 50, where x is the number of sundaes and y is the number of cones.
We can rearrange the inequality to solve for y:
3y ≤ 50 - 4x
y ≤ (50 - 4x)/3
This tells us that the maximum number of cones Ryleigh can buy is (50 - 4x)/3, given that she has already bought x sundaes.
To graph the solution to this inequality, we can plot the boundary line 4x + 3y = 50, which represents the maximum amount that Ryleigh can spend with her gift card. To plot the line, we can find two points on it by setting x to 0 and solving for y, and then setting y to 0 and solving for x:
When x = 0, we get:
4(0) + 3y = 50
y = 50/3
So one point on the line is (0, 50/3).
When y = 0, we get:
4x + 3(0) = 50
x = 12.5
So another point on the line is (12.5, 0).
We can plot these two points and draw a line through them to get the boundary line:
| * (12.5, 0)
|
|
3 | *
| *
| * (0, 50/3)
|________________________
0 10 20
Next, we need to shade the region of the graph that satisfies the inequality 4x + 3y ≤ 50. One way to do this is to test a point that is not on the boundary line, such as (0, 0):
4(0) + 3(0) = 0 ≤ 50
Since this point satisfies the inequality, we need to shade the region below the boundary line. Therefore, the correct graph is:
| * (12.5, 0)
| /
| /
3 | *
| /
| /
|/_______
0 10 20
The shaded region represents all the possible combinations of sundaes and cones that Ryleigh can buy with her gift card.
Explanation: