To solve the problem involving the given proportion, we use the property that states if two ratios are equal, their cross-products must also be equal. Here are the steps to find the distance [tex]\( x \)[/tex] between the lions and the monkeys:
1. Set up the proportion:
Given the proportion [tex]\(\frac{52}{78} = \frac{x}{96}\)[/tex], we need to find the value of [tex]\( x \)[/tex].
2. Cross-multiply:
To solve for [tex]\( x \)[/tex], we take the cross-products of the given ratios. That means we multiply the numerator of the first ratio by the denominator of the second ratio, and the denominator of the first ratio by the numerator of the second ratio. This gives us:
[tex]\[
52 \times 96 = 78 \times x
\][/tex]
3. Calculate the cross-product:
Performing the cross-multiplication, we get:
[tex]\[
52 \times 96 = 4992
\][/tex]
4. Divide to find [tex]\( x \)[/tex]:
We now have the equation:
[tex]\[
4992 = 78x
\][/tex]
To solve for [tex]\( x \)[/tex], divide both sides of the equation by 78:
[tex]\[
x = \frac{4992}{78}
\][/tex]
5. Compute the value:
Simplifying the division:
[tex]\[
x = 64
\][/tex]
So, the distance between the lions and the monkeys is [tex]\( 64 \)[/tex] feet.
