Question

8 from unit 4, lesson 3 in the 21st century, people measure length in feet and meters. at various points in history, people measured length in hands, cubits, and paces. there are 9 hands in 2 cubits. there are 5 cubits in 3 paces. a. write an equation to express the relationship between hands, h, and cubits, c. b. write an equation to express the relationship between hands, h, and paces, p.

Explanation:

Step1: Relate hands to cubits

Given 9 hands = 2 cubits, solve for $h$:
$h = \frac{9}{2}c$ or solve for $c$: $c = \frac{2}{9}h$

Step2: Relate cubits to paces

Given 5 cubits = 3 paces, solve for $c$:
$c = \frac{5}{3}p$

Step3: Substitute $c$ for hands-paces

Substitute $c = \frac{5}{3}p$ into $h = \frac{9}{2}c$:
$h = \frac{9}{2} \times \frac{5}{3}p = \frac{45}{6}p = \frac{15}{2}p$
Or solve for $p$: $p = \frac{2}{15}h$

Answer:

a. $\boldsymbol{h = \frac{9}{2}c}$ (or $\boldsymbol{c = \frac{2}{9}h}$)
b. $\boldsymbol{h = \frac{15}{2}p}$ (or $\boldsymbol{p = \frac{2}{15}h}$)