Question

The amount of money a worker makes varies directly with the hourly rate of pay. Worker A earns $168 for an 8 hour period. Worker B earns the same hourly rate as Worker A, but works for only 6 hours. What does Worker B earn?
A) $1008
B) $126
C) $1344
D) $160

Stuck on this one. Please explain?

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------$

$\bf \textit{money varies directly with hourly rate of pay}\qquad \stackrel{money}{m}=k\stackrel{hour~pay}{h} \\\\\\ \textit{we also know that } \begin{cases} m=168\\ h=8 \end{cases}\implies 168=k8\implies \cfrac{168}{8}=k \\\\\\ 21=k\qquad therefore\qquad \boxed{m=21h} \\\\\\ \textit{now, when h = 6, what is \underline{m}?}\qquad m=21(6)$