Question

a punch recipe calls for 3 cups of apple juice for every 4 cups of cranberry juice. jack uses 9 cups of apple juice and 13 cups of cranberry juice. did jack use the correct ratio for his recipe?
part a
find the ratio of apple juice to cranberry juice that the recipe states.
enter the correct answers in the boxes.
show hints
9 × cups of apple juice : 13 × cups of cranberry juice → \\(dfrac{9}{13}\\) ×

Explanation:

Step1: Identify recipe ratio

The recipe states apple juice to cranberry juice is $3:4$, or $\frac{3}{4}$.

Step2: Calculate Jack's ratio

Jack used 9 cups apple juice to 13 cups cranberry juice, so his ratio is $\frac{9}{13}$.

Step3: Compare the two ratios

Convert to common denominators:
$\frac{3}{4} = \frac{39}{52}$, $\frac{9}{13} = \frac{36}{52}$
Since $\frac{39}{52}
eq \frac{36}{52}$, the ratios are not equal.

Answer:

No, Jack did not use the correct ratio. The recipe's apple juice to cranberry juice ratio is $3:4$ ($\frac{3}{4}$), while Jack used a ratio of $9:13$ ($\frac{9}{13}$), which is not equivalent to the recipe ratio.