To find the correct number of children and adults that maintain the required ratio while having a total of 72 people on the playground, we first need to establish the ratio of children to adults based on the initial data.
From the table, we can see:
- For 24 children, there are 3 adults: the ratio is \( \frac{24}{3} = 8:1 \)
- For 40 children, there are 5 adults: the ratio is \( \frac{40}{5} = 8:1 \)
- For 48 children, there are 6 adults: the ratio is \( \frac{48}{6} = 8:1 \)
The ratio of children to adults is consistently \( 8:1 \).
Now, let \( c \) be the number of children and \( a \) be the number of adults. We can express this relationship as:
\[ \frac{c}{a} = 8 \]
This implies:
\[ c = 8a \]
Additionally, since the total number of people is 72, we have:
\[ c + a = 72 \]
We can substitute \( c = 8a \) into the total equation:
\[ 8a + a = 72 \]
Combine like terms:
\[ 9a = 72 \]
Now we can solve for \( a \):
\[ a = \frac{72}{9} = 8 \]
Now, substituting \( a \) back to find \( c \):
\[ c = 8a = 8 \times 8 = 64 \]
Thus, the number of children is \( 64 \) and the number of adults is \( 8 \).
The answer is D. 64 children and 8 adults.
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