The system of equations is ![t+b=25\\b=t+7](https://tex.z-dn.net/?f=t%2Bb%3D25%5C%5Cb%3Dt%2B7)
Step-by-step explanation:
We can answer this question as follows.
First of all, we call:
t = number of treadmills
b = number of stationary bikes
The two conditions that we have can be translated into equations as follows:
- The gym has a total of 25 treadmills and stationary bikes:
![t+b=25](https://tex.z-dn.net/?f=t%2Bb%3D25)
- There are seven more stationary bikes than treadmills:
![b=t+7](https://tex.z-dn.net/?f=b%3Dt%2B7)
So the system of equations to solve is
![t+b=25\\b=t+7](https://tex.z-dn.net/?f=t%2Bb%3D25%5C%5Cb%3Dt%2B7)
We now solve it in the following way: first, we rewrite the second equation by bringing t on the left side,
![t+b=25\\b-t=7](https://tex.z-dn.net/?f=t%2Bb%3D25%5C%5Cb-t%3D7)
Now we add the 1st equation to the 2nd equation:
![(t+b)+(b-t)=25+7\\t+b+b-t=32\\2b=32\\b=\frac{32}{2}=16](https://tex.z-dn.net/?f=%28t%2Bb%29%2B%28b-t%29%3D25%2B7%5C%5Ct%2Bb%2Bb-t%3D32%5C%5C2b%3D32%5C%5Cb%3D%5Cfrac%7B32%7D%7B2%7D%3D16)
And therefore,
![t+b=25\\t+16=25\\t=25-16=9](https://tex.z-dn.net/?f=t%2Bb%3D25%5C%5Ct%2B16%3D25%5C%5Ct%3D25-16%3D9)
So, there are 16 stationary bikes and 9 treadmills.
Learn more about systems of equations:
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