Question

Nick is given goes on a vacation with his savings, by day 5 he has spent 550, by day 9 he has spent 950. If he has 2250 how many days can he be on his vacation with the way he is spending?

Answer 1

Find a function that describes the expenses on Nick's vacations using the given information.

Use the number of days as the variable x and the expenses as the variable y.

According to the statement, 2 of the points in the function must be (5, 550) and (9, 950).

Find the slope of the line:

`m=(950-550)/(9-5)=(400)/(4)=100`

Now, use this slope and one of the given points in the point slope formula to find the equation of the line:

`\begin{gathered} y-y1=m(x-x1) \\ y-550=100(x-5) \\ y=100x-500+550 \\ y=100x+50 \end{gathered}`

This is the equation that describes the relationship between the days and the expenses on Nick's vacation.

The last step is to replace y for 2250 and solve for x, this way, you find the number of days he can be on his vacations with the way he is spending.

`\begin{gathered} 2250=100x+50 \\ 2250-50=100x \\ 2200=100x \\ (2200)/(100)=x \\ 22=x \\ x=22 \end{gathered}`

He can be 22 days on vacation with the way he is spending.