SOLUTION: We are working with substitution and elimination right now on story problems to solve systems of linear equations. I am not sure how you use ratios in equations like that. This

Algebra ->  Expressions-with-variables -> SOLUTION: We are working with substitution and elimination right now on story problems to solve systems of linear equations. I am not sure how you use ratios in equations like that. This      Log On


   

Question 25724: We are working with substitution and elimination right now on story problems to solve systems of linear equations. I am not sure how you use ratios in equations like that. This is the problem:
Kay spends 250 min/wk exercising. Her ratio of time spent on aerobics to time spent on weight training is 3 to 2. How many minutes per week does she spend on aerobics? How many minutes per week does she spend on weight training?
I'm sorry if this is already posted somewhere. I'm just not sure how to work the ratios into the equation. Thank you!!
Found 2 solutions by stanbon, rapaljer:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
aerobics to weight =3:2
So represent aerobics time as 3x and weight train as 2x
EQUATION:
3x+2x=250 min
5x=250
x=50
aerobics is 3x=150 min
Weight train is 2x=100 min
Cheers,
Stan H.

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = number of minutes on aerobics.
y = number of minutes on weight training

You need two equations:
x+y = 250
Then, set up a ratio +%28aerobics%29%2F%28weight+training%29+=3%2F2=x%2Fy, from which you get:
2x = 3y

x+y = 250
2x - 3y = 0

Multiply the first equation by 3:
3x + 3y = 750
2x - 3y = 0
5x = 750
x= 150 hours aerobics
y = 100 hours weight training

R^2 at SCC