Question

It takes 2 minutes to print out 3 photos. Write an equation relating the number of photos N to the number of minutes M. At this rate, how long will it take to print 10 photos? 14 photos?

Answer 1

Answer:

Part a) $M=6\frac{2}{3}\ min$

Part b) $M=9\frac{1}{3}\ min$

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 $k=\frac{N}{M}$ or $N=kM$

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

$k=\frac{N}{M}$

substitute the value of N and M

$k=\frac{3}{2}$

so

$N=\frac{3}{2}M$

Part a) How long will it take to print 10 photos?

For N=10

substitute in the linear equation

$10=\frac{3}{2}M$

solve for M

$M=\frac{10*2}{3}$

$M=\frac{20}{3}\ min$

Convert to mixed number

$M=\frac{20}{3}\ min=\frac{18}{3}+\frac{2}{3}=6\frac{2}{3}\ min$

Part b) How long will it take to print 14 photos?

For N=14

substitute in the linear equation

$14=\frac{3}{2}M$

solve for M

$M=\frac{14*2}{3}$

$M=\frac{28}{3}\ min$

Convert to mixed number

$M=\frac{28}{3}\ min=\frac{27}{3}+\frac{1}{3}=9\frac{1}{3}\ min$