Answer: 17 bicycles.
Step-by-step explanation:
In this case, "x" represents the number of bicycles at The Gym. We're going to name "y" the number of bicycles at Work-Out Corner. According to the data, Work-Out Corner has 5 more than 3 times as many exercise bicycles as The Gym, that can be represented by an equation:
[tex]y=3x+5[/tex]
As you can see, the equation given in the problem originates when you substitute "y" into the addition of the bicycles:
[tex]x+y=21\\x+3x+5=21[/tex]
Solving to find x (bicycles at The Gym):
[tex]4x=21-5\\x=\frac{16}{4}\\ x=4[/tex]
Then, you substitute that into the first equation and find y:
[tex]y=3(4)+5\\y=12+5\\y=17[/tex]
So, there are 17 bicycles at Work-Out Corner.
