For each pair of ratios below, make the two ratios equal.
?:4 $\stackrel{\text {-27: ww }}{2}$ : 3
The problem presents two equivalent ratios where one term is unknown. We denote the unknown value by \(x\), so the given proportion is written as \(\frac{x}{4} = \frac{27}{3}\). This represents a proportional relationship where the ratio of the unknown number to 4 is equal to the ratio of 27 to 3. To solve for \(x\), we first simplify the known ratio on the right side of the equation.
We simplify the ratio \(\frac{27}{3}\) by performing the division: \(\frac{27}{3} = 9\). Now the equation is simplified to \(\frac{x}{4} = 9\). To isolate \(x\), we multiply both sides of the equation by 4: \(x = 9 \times 4\). Carrying out this multiplication, we find \(x = 36\). Therefore, the unknown value in the ratio is 36.
Ratios are used frequently in daily life for scaling and consistency. For example, if you are making fruit punch and the recipe calls for 27 parts of water for every 3 parts of fruit concentrate, but you only have a container that holds 4 parts of concentrate, you can use the same ratio to determine how much water you need. By solving \(\frac{x}{4} = \frac{27}{3}\), you know that you need exactly 36 parts of water for your 4 parts of concentrate to maintain the perfect flavor balance.