Question

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

Answer 1

Answer:

N(h) = 2h + 6

Step-by-step explanation:

A model of the number of people that Denis can invite to his party:

N(x) = x/25.............(1)

Where x = amount of money saved

Amount of money saved can be modeled by the equation:

M(h) = 50h + 150...........(2)

In the above model, h = number of overtime hours

M(h) = amount of money saved = x

Therefore equation (1) can be re - written as:

N(x) = M(h)/25.................................(3)

Substituting equation (2) into equation (3)

$N(h) = \frac{50h + 150}{25} \\N(h) = \frac{50h}{25} + \frac{150}{25} \\N(h) = 2h + 6$

Find an explicit expression that models the number of people that Denis can invite to his party if he worked h  overtime hours this week can be expressed as:

N(h) = 2h + 6