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

Part a)
`M=6(2)/(3)\ min`

Part b)
`M=9(1)/(3)\ min`

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=(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=(N)/(M)`

substitute the value of N and M

`k=(3)/(2)`

so

`N=(3)/(2)M`

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

For N=10

substitute in the linear equation

`10=(3)/(2)M`

solve for M

`M=(10*2)/(3)`

`M=(20)/(3)\ min`

Convert to mixed number

`M=(20)/(3)\ min=(18)/(3)+(2)/(3)=6(2)/(3)\ min`

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

For N=14

substitute in the linear equation

`14=(3)/(2)M`

solve for M

`M=(14*2)/(3)`

`M=(28)/(3)\ min`

Convert to mixed number

`M=(28)/(3)\ min=(27)/(3)+(1)/(3)=9(1)/(3)\ min`