Question

Writing a Linear Function to Model a Scenario Pedro works as a newspaper deliverer. He receives a base pay plus an additional amount per newspaper delivered. Last week, Pedro delivered 5 newspapers and earned $37.50. This week, he delivered 20 newspapers and earned $75. Let x equal the number of newspapers Pedro delivers and y be the earnings he receives in dollars. Which linear function models the scenario?

Answer 1

Answer: y= 25+2.5x

Explanation:

Let a = base pay , b = additional amount per newspaper.

Given: Last week, Pedro delivered 5 newspapers and earned $37.50.

i.e. 37.50=a+5b (i)

This week, he delivered 20 newspapers and earned $75.

i.e. 75=a+20b (ii)

Eliminate (i) from (ii)

37.50=15b

`\Rightarrow\ b=(37.50)/(15)\\\\\Rightarrow\ b=2.5`, i.e. additional amount per newspaper= $2.5

Put b= 2.5 in (i)

`37.50=a+5(2.5)\\\\\Rightarrow\ 37.50=a+12.5\\\\\Rightarrow\ a=37.50-12.5\\\\\Rightarrow\ a=25`, i.e. base pay = $20

Let x= Number of newspapers Pedro delivers.

y= Earnings he receives in dollars.

y= 25+2.5x will be the required function.