Question

Planning a Birthday Party!

You are helping a friend plan her party at a bowling alley. The bowling alley offers different birthday party packages: Package A is represented by the function C = 7p + 5 where c is the total cost and p is the number of people. Package B is represented in the table.

Number of People, Total Cost $
1 person- 12.50
2 person- 19.00
3 person- 25.50
4 person- 32.00
Which package your friend should choose if she wants to invite 12 people?

Answer 1

So for the second table, we have to figure out the equation. I'll be putting the equation into slope-intercept form. (c = mp+b, m = slope and b = y-intercept).

To get the slope for the table, the formula is
`(y_2-y_1)/(x_2-x_1)` . For this I'll be using (1,12.50) and (4,32).
`(32-12.50)/(4-1)=(19.50)/(3)=6.50`

Now that we have our slope, we can solve for the y-intercept. For this you need one of the points to replace the c and p placeholder, and for this I'll be using (2,19).

`19=6.5(2)+b\\ 19=13+b\\ 6=b`

Now that we have all our info, we can form the Package B equation as such: c = 6.5p + 6

Now that we have both equations, just plug in 12 into the p placeholder for both and solve:

`c=7(12)+5\\ c=84+5\\ c=89`

`c=6.5(12)+6\\ c=78+6\\ c=84`

Assuming that our friend wants to save money, they should choose Package B.

Answer 2

We can find the more suitable one by comparing the cost for 12 people:

The cost of package A:
=7(12)+5
=84+5
=$89

The cost of package B:
=(12÷4)×32
=3×32
=$96

Because Package B is more expensive than package A($96>$89), She should choose package A.

Hope it helps!