Question

A coach plans to order new volleyballs and soccer balls.

The cost of each volleyball is $20.
The cost of each soccer ball is $25.
The coach plans to order at least 50 volleyballs and soccer balls in all.
The coach can spend a maximum of $1,100.
Which graph represents x, the number of volleyballs, and y, the number of soccer balls that the coach can order?

Answer 1

Let x = number of volleyballs and y = number of soccer balls.

Inequalities:
- Cost: 20x + 25y ≤ 1100 => 4x + 5y ≤ 220 => y ≤ 44 − 0.8x
- Total at least 50: x + y ≥ 50 => y ≥ 50 − x
- Nonnegative: x ≥ 0, y ≥ 0

Key points:
- Quantity line x + y = 50 has intercepts (0,50) and (50,0).
- Cost line 4x + 5y = 220 has intercepts (0,44) and (55,0).
- The two lines meet at (30,20).

Feasible region: the area in the first quadrant that lies above the line y = 50 − x and below the line y = 44 − 0.8x. This region is the triangle with vertices (30,20), (50,0), and (55,0).

So the correct graph shows the two lines y = 50 − x and y = 44 − 0.8x and shades the triangular region between them (above the first line, below the second) with x,y ≥ 0.