Question

which equality represents the proportion $8 is to 11 cans as $16 is to 22 cans?
a. \\(\frac{\\$8}{22\text{ cans}} = \frac{11\text{ cans}}{\\$16}\\)
b. \\(\frac{\\$8}{11\text{ cans}} = \frac{\\$16}{22\text{ cans}}\\)
c. \\(\frac{\\$8}{22\text{ cans}} = \frac{\\$16}{11\text{ cans}}\\)
d. \\(\frac{\\$8}{11\text{ cans}} = \frac{22\text{ cans}}{\\$16}\\)

Explanation:

Step1: Understand the proportion

The problem states that $8 is to 11 cans as $16 is to 22 cans. In proportion terms, this means the ratio of $8 to 11 cans should be equal to the ratio of $16 to 22 cans. So we can write this as $\frac{\$8}{11\ \text{cans}}=\frac{\$16}{22\ \text{cans}}$.

Step2: Match with options

Now we check each option:

• Option A: $\frac{\$8}{22\ \text{cans}}=\frac{11\ \text{cans}}{\$16}$ – Incorrect, as the ratios are not set up correctly.
• Option B: $\frac{\$8}{11\ \text{cans}}=\frac{\$16}{22\ \text{cans}}$ – This matches our derived proportion.
• Option C: $\frac{\$8}{22\ \text{cans}}=\frac{\$16}{11\ \text{cans}}$ – Incorrect, ratios are reversed and mismatched.
• Option D: $\frac{\$8}{11\ \text{cans}}=\frac{22\ \text{cans}}{\$16}$ – Incorrect, units and ratios are mismatched.

Answer:

B. $\boldsymbol{\frac{\$8}{11\ \text{cans}}=\frac{\$16}{22\ \text{cans}}}$