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.



The graph represents x, the number of volleyballs, and y, the number of soccer balls that the coach can order.

Multiple Choice Question
Which of the following ordered pairs is a solution to the graph of the system of inequalities?
A.
(13, 35)
B.
(51, 3)
C.
(5, 50)
D.
(3, 51)

Answer 1

To determine which of the ordered pairs is a solution to the graph of the system of inequalities, we need to establish the inequalities based on the given information.

1. **Total quantity constraint**:
The coach plans to order at least 50 volleyballs and soccer balls combined:
\[
x + y \geq 50
\]

2. **Budget constraint**:
The coach can spend a maximum of $1,100:
\[
20x + 25y \leq 1100
\]

Now let's evaluate each option to see if it satisfies both inequalities.

**Option A: (13, 35)**
- Total: \(13 + 35 = 48\) (which does not satisfy \(x + y \geq 50\))
- Budget: \(20(13) + 25(35) = 260 + 875 = 1135\) (which does not satisfy \(20x + 25y \leq 1100\))

**Option B: (51, 3)**
- Total: \(51 + 3 = 54\) (satisfies \(x + y \geq 50\))
- Budget: \(20(51) + 25(3) = 1020 + 75 = 1095\) (satisfies \(20x + 25y \leq 1100\))

**Option C: (5, 50)**
- Total: \(5 + 50 = 55\) (satisfies \(x + y \geq 50\))
- Budget: \(20(5) + 25(50) = 100 + 1250 = 1350\) (which does not satisfy \(20x + 25y \leq 1100\))

**Option D: (3, 51)**
- Total: \(3 + 51 = 54\) (satisfies \(x + y \geq 50\))
- Budget: \(20(3) + 25(51) = 60 + 1275 = 1335\) (which does not satisfy \(20x + 25y \leq 1100\))

Based on this analysis, the only ordered pair that satisfies both inequalities is:

**B. (51, 3)**