To determine which of the labeled points (if any) is a viable solution for the inequality \( 25z + 15y \geq 200 \), we first need to express the inequality in terms of the variables provided. In your context, it looks like there might be a mistake in the variable names—let's assume \( z \) should actually be \( x \) (the number of lawns mowed) and \( y \) (the number of dogs walked). Therefore, the inequality you want to check is:
\[ 25x + 15y \geq 200 \]
Next, we'll test each of the given points \( (2,3) \), \( (20, 11.5) \), and \( (10, 10) \):
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For (2, 3): \[ 25(2) + 15(3) = 50 + 45 = 95 \] \[ 95 \geq 200 \quad \text{(false)} \]
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For (20, 11.5): \[ 25(20) + 15(11.5) = 500 + 172.5 = 672.5 \] \[ 672.5 \geq 200 \quad \text{(true)} \]
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For (10, 10): \[ 25(10) + 15(10) = 250 + 150 = 400 \] \[ 400 \geq 200 \quad \text{(true)} \]
Now, let's summarize the results:
- Point \( (2, 3) \): Not a solution
- Point \( (20, 11.5) \): Viable solution
- Point \( (10, 10) \): Viable solution
Given this analysis, both points \( (20, 11.5) \) and \( (10, 10) \) are viable solutions for the inequality \( 25x + 15y \geq 200 \).
Since the question asks for which of the labeled points is a viable solution in this context, it would be correct to say that both (20, 11.5) and (10, 10) are viable solutions. If you must choose just one point, then either valid choice can be considered correct depending on the context of the question.
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