Question

The number of people, NNN, that Denis can invite to his party is dependent on the amount of money, xxx, in dollars, that he saved up for the party and can be modeled by the function N(x) = \dfrac{x}{25}N(x)= 25 x ​ N, left parenthesis, x, right parenthesis, equals, start fraction, x, divided by, 25, end fraction. The amount of money that Denis saved for the party, MMM, in dollars, is dependent on the number of overtime hours, hhh, he worked this week and can be modeled by the function M(h)=50h+150M(h)=50h+150M, left parenthesis, h, right parenthesis, equals, 50, h, plus, 150. Find an explicit expression that models the number of people that Denis can invite to his party if he worked hhh overtime hours this week.

Answer 1

N(h)=2h+6

Explanation:

The number of people, N, that Denis can invite to his party is dependent on the amount of money, x, in dollars that he saved up for the party and can be modeled by the function:

`N(x) = (x)/(25)`

The amount of money that Denis saved for the party, M, in dollars, is dependent on the number of overtime hours, h, he worked this week and can be modeled by the function:

M(h)=50h+150

We want to determine an explicit expression that models the number of people that Denis can invite to his party if he worked h overtime hours this week.

When x=M(h)

`N(M(h)) = (50h+150)/(25)\\N(h)=(25(2h+6))/(25)\\N(h)=2h+6`

The required function is:

`N(h)=2h+6`