Question

emma is preparing for a multi-day hiking trip. the number of protein bars she needs to pack varies directly with the total number of miles she plans to hike. on her last trip, she hiked 42 miles and packed 7 protein bars. on this trip, she plans to hike 30 miles. how many protein bars should she pack? protein bars submit

Explanation:

Step1: Define direct variation

Let $p$ = number of protein bars, $m$ = miles. Direct variation: $p = km$, where $k$ is constant.

Step2: Solve for constant $k$

Use $m=42$, $p=7$:
$7 = k \times 42$
$k = \frac{7}{42} = \frac{1}{6}$

Step3: Calculate protein bars for 30 miles

Substitute $m=30$, $k=\frac{1}{6}$:
$p = \frac{1}{6} \times 30$

Answer:

5 protein bars