On average, a certain tree grows 51 centimeters every m months. At this rate, which expression represents the number of centimeters, on average, the tree grows every k years?

On average, a certain tree grows 51 centimeters every m months. At this rate, which... | SAT Ratios, rates, proportional relationships, and units Practice

Answer: [D] $\dfrac{612k}{m}$

Explanation:1. Determine the growth rate in centimeters per month: The tree grows $51$ centimeters in m months. Growth rate = $\dfrac{51 \text{ cm}}{m \text{ months}}$ .

Convert k years into months: There are $12$ months in $1$ year. So, k years = $k \times 12 = 12k$ months.
Calculate the total growth in $12k$ months (which is k years): Total growth = Growth rate $\times$ Number of months. Total growth = $\left(\dfrac{51}{m}\right) \dfrac{\text{cm}}{\text{month}} \times (12k) \text{ months}$ . Total growth = $\dfrac{51 \times 12k}{m}$ cm.
Simplify the expression: $51 \times 12 = 51 \times (10 + 2) = 510 + 102 = 612$ . So, Total growth = $\dfrac{612k}{m}$ cm.

Conclusion:The expression that represents the number of centimeters the tree grows every k years is $\dfrac{612k}{m}$ .

Question Bank

Question Bank

SAT Ratios, rates, proportional relationships, and units practice question

Explanation