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