pleeease help me on this word problem. I've been trying to figure it out for a while and i just cant get it.

Question

When using a stair climber; Eric burns 9.6 calories per minute. When he walks on the treadmill, he burns 5.3 calories per minute. If Eric has 50 minutes to exercise and wants to burn 350 calories, how many minutes should he spend on each machine?

Answer 1

Let s= minutes on stair climber
Let t= minutes on treadmill
minutes on climber + minutes on treadmill must be 50
We write this as s+t=50
Calories burned on climber is cal./ min. X min.
This is 9.6(s)
Calories burned on treadmill is cal./min. X min.
This is 5.3(t)
Total calories burned is to be 350.
We write this as 9.6s+5.3t=350
We have our 2 equations.

s+t=50
9.6s+5.3t=350
From s+t=50, s=50-t
Substitute this into the second equation for s to get
9.6(50-t)+5.3t=350
480-9.6t + 5.3t=350
-4.3t= -130
t=30.2
Since s+t=50, s=50-30.2=19.8
30.2 minutes on treadmill, 19.8 minutes on climber

Verify answer:
30.2(5.3)+19.8(9.6) = 190+160 = 350 calories
I hope this helps.

Answer 2

x = minutes on stair climber
50-x = minutes on treadmill
So 9.6x+ 5.3(50-x) = 350
9.6x + 265 -5.3x = 350
4.3x = 85
x = 19.77 minutes on stair climber
50-x = 30.23 minutes on treadmill