Answer:
Franchise has 11 quarters and 16 dimes.
Step-by-step explanation:
Let d represent number of dimes and q represent number of quarters.
We have been given that the number of dimes is five more than the number of quarters. We can represent this information in an equation as:
![d=q+5...(1)](https://tex.z-dn.net/?f=d%3Dq%2B5...%281%29)
We are also told that Francine has $4.35 in dimes and quarters. We can represent this information in an equation as:
![0.10d+0.25q=4.35...(2)](https://tex.z-dn.net/?f=0.10d%2B0.25q%3D4.35...%282%29)
Now, we will substitution method to solve linear equations. Upon substituting equation (1) in equation (2), we will get:
![0.10(q+5)+0.25q=4.35](https://tex.z-dn.net/?f=0.10%28q%2B5%29%2B0.25q%3D4.35)
![0.10q+0.50+0.25q=4.35](https://tex.z-dn.net/?f=0.10q%2B0.50%2B0.25q%3D4.35)
![0.35q+0.50=4.35](https://tex.z-dn.net/?f=0.35q%2B0.50%3D4.35)
![0.35q+0.50-0.50=4.35-0.50](https://tex.z-dn.net/?f=0.35q%2B0.50-0.50%3D4.35-0.50)
![0.35q=3.85](https://tex.z-dn.net/?f=0.35q%3D3.85)
![\frac{0.35q}{0.35}=\frac{3.85}{0.35}](https://tex.z-dn.net/?f=%5Cfrac%7B0.35q%7D%7B0.35%7D%3D%5Cfrac%7B3.85%7D%7B0.35%7D)
![q=11](https://tex.z-dn.net/?f=q%3D11)
Therefore, Franchise has 11 quarters.
Upon substituting
in equation (1), we will get:
![d=11+5](https://tex.z-dn.net/?f=d%3D11%2B5)
![d=16](https://tex.z-dn.net/?f=d%3D16)
Therefore, Franchise has 16 dimes.