Solve the problem.
-If $\mathrm { m }$ varies directly as $\mathrm { x }$ and $\mathrm { y }$, and $\mathrm { m } = 24$ when $\mathrm { x } = 6$ and $\mathrm { y } = 9$, find $\mathrm { m }$ when $\mathrm { x } = 15$ and $\mathrm { y } = 8$.
A) $\frac { 140 } { 3 }$
B) $\frac { 64 } { 3 }$
C) $\frac { 160 } { 3 }$
D) 60

Question

Quizplus · Accepted Answer

Since $m$ varies directly as $x$ and $y$, we can write $m = kxy$ for some constant $k$. Given $m = 24$ when $x = 6$ and $y = 9$, we find $k$ by substituting these values: $24 = k \cdot 6 \cdot 9$, so $k = \frac{24}{54} = \frac{4}{9}$. To find $m$ when $x = 15$ and $y = 8$, substitute these values and $k$ into the original equation: $m = \frac{4}{9} \cdot 15 \cdot 8 = \frac{4 \cdot 15 \cdot 8}{9} = \frac{480}{9} = \frac{160}{3}$.

Solve the Problem m\mathrm { m }m Varies Directly As x\mathrm { x }x

Solve the Problem $\mathrm { m }$ Varies Directly As $\mathrm { x }$