Answer:
Part a) [tex]M=6\frac{2}{3}\ min[/tex]
Part b) [tex]M=9\frac{1}{3}\ min[/tex]
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 [tex]k=\frac{N}{M}[/tex] or [tex]N=kM[/tex]
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
[tex]k=\frac{N}{M}[/tex]
substitute the value of N and M
[tex]k=\frac{3}{2}[/tex]
so
[tex]N=\frac{3}{2}M[/tex]
Part a) How long will it take to print 10 photos?
For N=10
substitute in the linear equation
[tex]10=\frac{3}{2}M[/tex]
solve for M
[tex]M=\frac{10*2}{3}[/tex]
[tex]M=\frac{20}{3}\ min[/tex]
Convert to mixed number
[tex]M=\frac{20}{3}\ min=\frac{18}{3}+\frac{2}{3}=6\frac{2}{3}\ min[/tex]
Part b) How long will it take to print 14 photos?
For N=14
substitute in the linear equation
[tex]14=\frac{3}{2}M[/tex]
solve for M
[tex]M=\frac{14*2}{3}[/tex]
[tex]M=\frac{28}{3}\ min[/tex]
Convert to mixed number
[tex]M=\frac{28}{3}\ min=\frac{27}{3}+\frac{1}{3}=9\frac{1}{3}\ min[/tex]
