To solve the problem of finding the number that makes the ratio 9:x equivalent to the ratio 1:8, we follow these steps:
1. Set Up the Ratio Equation:
We start by setting up the equation based on the given ratios. According to the problem, the ratio of 9 to x should be equivalent to the ratio of 1 to 8. We can write this as:
[tex]\[
\frac{1}{8} = \frac{9}{x}
\][/tex]
2. Cross-Multiply to Solve for x:
To eliminate the fractions, we use cross-multiplication. This means we multiply the numerator of one side by the denominator of the other side, and do the same for the other pair:
[tex]\[
1 \cdot x = 9 \cdot 8
\][/tex]
3. Simplify the Equation:
Now, simplify the equation:
[tex]\[
x = 72
\][/tex]
Therefore, the number that makes the ratio 9:x equivalent to the ratio 1:8 is 72.
