Answer:
Part a) ![M=6\frac{2}{3}\ min](https://tex.z-dn.net/?f=M%3D6%5Cfrac%7B2%7D%7B3%7D%5C%20min)
Part b) ![M=9\frac{1}{3}\ min](https://tex.z-dn.net/?f=M%3D9%5Cfrac%7B1%7D%7B3%7D%5C%20min)
Step-by-step explanation:
we know that
A relationship between two variables, M, and N, represent a proportional variation if it can be expressed in the form
or ![N=kM](https://tex.z-dn.net/?f=N%3DkM)
In this problem, the relationship between the number of photos N to the number of minutes M represent a proportional variation
we have that
For M=2, N=3
Find the the constant of proportionality k
![k=\frac{N}{M}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7BN%7D%7BM%7D)
substitute the value of N and M
![k=\frac{3}{2}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B3%7D%7B2%7D)
so
![N=\frac{3}{2}M](https://tex.z-dn.net/?f=N%3D%5Cfrac%7B3%7D%7B2%7DM)
Part a) How long will it take to print 10 photos?
For N=10
substitute in the linear equation
![10=\frac{3}{2}M](https://tex.z-dn.net/?f=10%3D%5Cfrac%7B3%7D%7B2%7DM)
solve for M
![M=\frac{10*2}{3}](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B10%2A2%7D%7B3%7D)
![M=\frac{20}{3}\ min](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B20%7D%7B3%7D%5C%20min)
Convert to mixed number
![M=\frac{20}{3}\ min=\frac{18}{3}+\frac{2}{3}=6\frac{2}{3}\ min](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B20%7D%7B3%7D%5C%20min%3D%5Cfrac%7B18%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B3%7D%3D6%5Cfrac%7B2%7D%7B3%7D%5C%20min)
Part b) How long will it take to print 14 photos?
For N=14
substitute in the linear equation
![14=\frac{3}{2}M](https://tex.z-dn.net/?f=14%3D%5Cfrac%7B3%7D%7B2%7DM)
solve for M
![M=\frac{14*2}{3}](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B14%2A2%7D%7B3%7D)
![M=\frac{28}{3}\ min](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B28%7D%7B3%7D%5C%20min)
Convert to mixed number
![M=\frac{28}{3}\ min=\frac{27}{3}+\frac{1}{3}=9\frac{1}{3}\ min](https://tex.z-dn.net/?f=M%3D%5Cfrac%7B28%7D%7B3%7D%5C%20min%3D%5Cfrac%7B27%7D%7B3%7D%2B%5Cfrac%7B1%7D%7B3%7D%3D9%5Cfrac%7B1%7D%7B3%7D%5C%20min)