Question

on monday, jessica runs on a track at her school. each day from tuesday through friday, she runs $1\frac{1}{2}$ mi in a park. the total distance she runs for the week is 8 mi. solve the equation $m + 4\left(1\frac{1}{2}\
ight) = 8$ to find the number of miles, $m$, jessica runs on monday. show your work.

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(1\frac{1}{2}\) to an improper fraction. \(1\frac{1}{2}=\frac{3}{2}\). So the equation becomes \(m + 4\times\frac{3}{2}=8\).

Step2: Simplify the multiplication term

Calculate \(4\times\frac{3}{2}\). \(4\times\frac{3}{2}=\frac{4\times3}{2}=\frac{12}{2} = 6\). Now the equation is \(m+6 = 8\).

Step3: Solve for m

Subtract 6 from both sides of the equation. \(m+6 - 6=8 - 6\), which simplifies to \(m = 2\).

Answer:

The number of miles Jessica runs on Monday is \(2\) miles.