Question

word problem: I run 7 times as far as I swim. I bike 3 times as far as I run. One week I totaled 232 miles. How far did I run?

Answer 1

r = miles run
s = miles swam
b = miles biked

r = 7s
b = 3r

total = b + r + s = 232
therefore: 3r + r + (r/7) = 232 <--- solve this to find r

Answer 2

I am supposed to solve using a system of equations. I see how to solve the 2nd equation you wrote, but how can I solve by elimination or substitution?

Answer 3

we eliminated b and s to get the last equation.

Answer 4

using b = 3r
and s = r / 7

Answer 5

basically you have 3 equations:
1. r = 7s
2. b = 3r
3. b + r + s = 232

Answer 6

we used 1 and 2 to eliminate b and s from the 3rd equation.

Answer 7

That makes sense! Thank you!!

Answer 8

yw