Chapter 5.2, Problem 25P

Tell whether the two quantities vary directly. Explain your reasoning.

Jackson’s age and Dylan’s age

To determine

To Explain: Whether the two given quantities vary directly or not.

Answer to Problem 25P

No! They are not directly vary.Because the ratio of their ages are not constant.

Explanation of Solution

Given information: Jackson’s age and Dylan’s age.

Let in 2020, Jackson’s age is 10 years and Dylan’s age is 12 years.

In 2026, Jackson’s age will be 16 years and Dylan’s age will be 18 years.

In 2030, Jackson’s age will be 20 years and Dylan’s age will be 22 years.

Difference in their age is constant because

In 2020, $12-10=2$ years

In 2026, $18-16=2$ years

In 2030, $22-20=2$ years.

But ratio of their ages

In 2020, $\frac{10}{12}=\mathrm{0.833...}$

In2026, $\frac{16}{18}=\mathrm{0.888...}$

In 2030, $\frac{20}{22}=\mathrm{0.909...}$

Ratio of their age is not constant.

Conclusion: Their age are not direct variation.