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?

(1 point)








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Answer 1

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

Inequalities:
- At least 50 balls: x + y ≥ 50
- At most $1,100: 20x + 25y ≤ 1100 (or 4x + 5y ≤ 220)
- x ≥ 0, y ≥ 0

Lines and intercepts:
- x + y = 50 has intercepts (50,0) and (0,50). The feasible side is on or above this line.
- 4x + 5y = 220 has intercepts (55,0) and (0,44). The feasible side is on or below this line.

The feasible region is the triangular region with vertices at (30,20) (the intersection of the two lines), (50,0), and (55,0). So the correct graph shades the triangle bounded by the line x + y = 50, the line 4x + 5y = 220, and the x-axis between x = 50 and x = 55.