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Answer :
Let's go through the problem step-by-step to understand how to identify the correct equation to find the length of the deep end of the swimming pool.
We are given that the area of the surface of the swimming pool is 210 square feet. Let's denote the length of the deep end by [tex]\(d\)[/tex] and assume the width of the pool is a known value; we will use the equations provided to find [tex]\(d\)[/tex].
We need to consider the equations one by one:
1. [tex]\(210 - 10 = 9d\)[/tex]
- This equation suggests that subtracting 10 from 210 equals 9 times the length of the deep end, which does not logically describe the relationship between the area, length, and width of the pool.
2. [tex]\(210 = 10 + 9 + d\)[/tex]
- This equation indicates that the total area equals the sum of the width, an unknown value 9, and the length of the deep end, which doesn't clearly represent a standard formula for calculating the area of a pool.
3. [tex]\(9d \times 10 = 210\)[/tex]
- This equation indicates that the product of 9 times the length of the deep end (d) and the width (10) equals the total area of the pool. This setup correctly follows the area formula [tex]\( \text{Area} = \text{length} \times \text{width} \)[/tex].
4. [tex]\(10d + 10 \times 9 = 210\)[/tex]
- This equation implies combining products of terms, which does not correctly represent the standard area calculation for a rectangle or pool.
Clearly, the equation that makes the most sense for calculating the area of the pool is:
[tex]\[ 9d \times 10 = 210 \][/tex]
To solve for the length of the deep end ([tex]\(d\)[/tex]), we follow these steps:
[tex]\[ 9d \times 10 = 210 \][/tex]
First, simplify the multiplication on the left side:
[tex]\[ 90d = 210 \][/tex]
Next, isolate [tex]\(d\)[/tex] by dividing both sides by 90:
[tex]\[ d = \frac{210}{90} \][/tex]
Simplify the fraction:
[tex]\[ d = \frac{21}{9} = \frac{7}{3} \approx 2.33 \text{ feet} \][/tex]
So, the length of the deep end of the swimming pool is approximately [tex]\(2.33\)[/tex] feet.
We are given that the area of the surface of the swimming pool is 210 square feet. Let's denote the length of the deep end by [tex]\(d\)[/tex] and assume the width of the pool is a known value; we will use the equations provided to find [tex]\(d\)[/tex].
We need to consider the equations one by one:
1. [tex]\(210 - 10 = 9d\)[/tex]
- This equation suggests that subtracting 10 from 210 equals 9 times the length of the deep end, which does not logically describe the relationship between the area, length, and width of the pool.
2. [tex]\(210 = 10 + 9 + d\)[/tex]
- This equation indicates that the total area equals the sum of the width, an unknown value 9, and the length of the deep end, which doesn't clearly represent a standard formula for calculating the area of a pool.
3. [tex]\(9d \times 10 = 210\)[/tex]
- This equation indicates that the product of 9 times the length of the deep end (d) and the width (10) equals the total area of the pool. This setup correctly follows the area formula [tex]\( \text{Area} = \text{length} \times \text{width} \)[/tex].
4. [tex]\(10d + 10 \times 9 = 210\)[/tex]
- This equation implies combining products of terms, which does not correctly represent the standard area calculation for a rectangle or pool.
Clearly, the equation that makes the most sense for calculating the area of the pool is:
[tex]\[ 9d \times 10 = 210 \][/tex]
To solve for the length of the deep end ([tex]\(d\)[/tex]), we follow these steps:
[tex]\[ 9d \times 10 = 210 \][/tex]
First, simplify the multiplication on the left side:
[tex]\[ 90d = 210 \][/tex]
Next, isolate [tex]\(d\)[/tex] by dividing both sides by 90:
[tex]\[ d = \frac{210}{90} \][/tex]
Simplify the fraction:
[tex]\[ d = \frac{21}{9} = \frac{7}{3} \approx 2.33 \text{ feet} \][/tex]
So, the length of the deep end of the swimming pool is approximately [tex]\(2.33\)[/tex] feet.
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