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]
