Question

Daniel wants to spend $146 on his accomadation. Cost per night is $54 dollars. On line booking company charges a 1 time fee of $38 dollars. How many nights would he have stayed?

Answer 1

2 nights

Explanation:

Type of equation to model the problem:

We can model the situation using a linear equation, superficially slope-intercept form whose general equation is given by:

y = mx + b, where

• m is the slope (change in y / change in x),
• and b is the y-intercept.

Explaining y and x in context of the problem:

• The problem indicates that cost if a function of nights.

• This means that cost depends on the amount of nights.

Therefore, cost is the y value and the number of nights is the x value.

Identifying the slope:

• The slope is $54, since cost increases by $54 per each night Daniel stays.

Identifying the y-intercept:

• The y-intercept is $38, since Daniels pays this amount even if he stays 0 nights.

Determining the amount of nights Daniel must stay to have a cost of $146:

Now we can substitute 146 for y, 54 for m, and 38 for b in the slope-intercept form to find x, the number of nights:

(146 = 54x + 38) - 38

(108 = 54x) / 54

2 = x

Thus, Daniel would have stayed 2 nights to have a cost of $146.