Question

The playground guidelines at Hillside Elementary School require a certain ratio of children to adults. The number of children, adults, and total people that can be on the playground are shown in the part-to-part-to-whole ratio table below.

Children 24 40 48 ?
Adults 3 5 6 ?
Total People 27 45 54 72

If there are a total of 72 people on the playground, how many children and adults should there be to maintain the correct ratio?

A.
62 children and 10 adults

B.
56 children and 7 adults

C.
72 children and 9 adults

D.
64 children and 8 adults

Answer 1

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**.