Carly is training for a triathlon. In her training routine each week, she runs 7 times as far as she swims, and bikes 3 times as far as she runs. One week she trained a total of 232. How far did she run that week?

Answer: [tex]56[/tex]Step-by-step explanation: Let be "s" the distance Carly swam that week, "b" the distance Carly bikes and "r" the distance Carly ran that week. According to the exercise: [tex]s+b+r=232[/tex]     [Equation 1] We know that she runs 7 times as far as she swims; then: [tex]r=7s[/tex]       [Equation 2] Since she bikes 3 times as far as she runs: [tex]b=3r[/tex]      [Equation 3] The steps to solve this are: - Solve for "s" from the [Equation 2]: [tex]r=7s\\\\s=\frac{r}{7}[/tex] - Substitute this into [Equation 1]. - Substitute [Equation 3] into [Equation 1]. Then: [tex]\frac{r}{7}+3r+r=232[/tex] - Solve for "r": [tex]\frac{r}{7}+3r+r=232\\\\r(\frac{1}{7}+3+1)=232\\\\\frac{29}{7}r=232\\\\r=(232)(\frac{7}{29})\\\\r=56[/tex]