Functions in Real Life: Wedding Planning Math
This amazing math wedding cake is from Pink Cake Box.
This past week, I was attempting to plan a wedding, and came across yet another “GRE math in real life” situation. (When you’re a GRE instructor, you tend to spot these quite often!)
I’m going to give you three different GRE math problems using the same real-life wedding scenario. Here goes!
Question 1: To hold a wedding at NYC Private Club costs $130 per person, including food and open bar. There is also a $500 ceremony fee and a 20% service charge, as well as 8.875% NYC tax on the entire bill. Which of the following represents the total cost C of a wedding at NYC Private Club as a function of the number of people, p?
A. C(p) = (130p + 500)(0.8)(91.125)
B. C(p) = (130p)(0.2)(1.08875) + 500
C. C(p) = (130p)(1.2)(0.08875) + 500
D. C(p) = 130p + 1.2p + 1.08875p + 500
E. C(p) = (130p + 500)(1.2)(1.08875)
Question 2: To hold a wedding at NYC Private Club costs $130 per person, including food and open bar. There is also a $500 ceremony fee and a 20% service charge, as well as 8.875% NYC tax on the entire bill. If a wedding at NYC Private Club cost, to the nearest dollar, $10,334, how many guests attended the wedding?
Question 3:
To hold a wedding at NYC Private Club costs $130 per person, including food and open bar. There is also a $500 ceremony fee and a 20% service charge, as well as 8.875% NYC tax on the entire bill.
Quantity A The overall cost per person, including all fees, charges, and taxes, of a wedding at NYC Private Club with 100 guests | Quantity B The overall cost per person, including all fees, charges, and taxes, of a wedding at NYC Private Club with 150 guests |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Select your answers before reading any further!
Question 1: The tricky thing about this function is that the cost of $130 is per person, whereas the $500 is simply a flat fee. Also, the service charge and tax need to be applied to the entire amount, not just the $130 per person.
So, 130p takes care of the $130 per person. Then, add $500. (130p + 500) is the total cost without the service charge and tax. To add 20%, multiply by 1.2 (NOT just 0.2, which would make the number SMALLER. We want to KEEP the original amount, then add ANOTHER 20% to it.) To add 8.875%, multiply by 1.08875 (for the same reason).
Thus, the correct function is C(p) = (130p + 500)(1.2)(1.08875), or answer choice E.
Question 2: Once you’ve done Question 1, Question 2 should seem a bit easier — it’s basically question 1 in reverse. On your paper, you would need to write a formula for the wedding cost, and set the answer equal to $10,334:
(130p + 500)(1.2)(1.08875) = 10334
Let’s multiply (1.2)(1.08875) to get 1.3065, then divide both sides by 1.3065:
(130p + 500)(1.3065) = 10334
130p + 500 = 7909.682357
130p = 7409.682357
p = 56.9975566
Hmmn, 56.9975566 people? Remember that the cost was rounded to the nearest dollar, which is why our answer is pretty close to 57, but not exactly. You might do a little logic check to make sure it’s okay to round up (it is) — it turns out that $10,334 is enough to pay for 56 and more than 99/100ths of another person. So, does it make sense that less-than-one-more-dollar would pay for the other less-than-1% of a person? Why yes, it does!
The answer is 57.
Question 3: Like many Quantitative Comparison questions, this question requires NO MATH, just a bit of logic.
Obviously, the more people at the wedding, the higher the cost. But wouldn’t the cost PER PERSON stay the same? Not at NYC Private Club. While the $130 is per person and the service charge and tax are proportional to the number of people, the $500 doesn’t change based on how many people you have.
Imagine you had a wedding with only one guest. The cost per person would be $130, plus $500, plus service charge and tax! But if you had a wedding with 500 guests, the cost per person would be $130, plus $1 (1/500th of the $500 fee), plus service charge and tax.
So, the more people you have, the lower the cost per person. The answer is A. (Don’t get tricked! Column B represents a better deal (at least per person), but we need to pick the largest number, of course!)
In sum, the GRE is hard and weddings are expensive. Okay, just kidding: the GRE is completely learnable, and weddings are expensive.