Doug and Dave shared a pizza with equally-sized slices. Doug wanted a plain pizza, but Dave wanted anchovies on half the pizza. The cost of a plain pizza was dollars, and there was an additional cost of dollars for putting anchovies on one half. Dave ate all the slices of anchovy pizza and one plain slice. Doug ate the remainder. Each paid for what he had eaten. How many more dollars did Dave pay than Doug?
- A)
- B)
- C)
- D)
- E)
Answer
D
Key insight
Price per slice: plain slices cost 1 dollar, the anchovy half costs 4 + 2 = 6 for four slices; Dave pays 7, Doug pays 3.
Solution
The plain pizza is dollars for slices, so each slice carries dollar of base cost. The -dollar anchovy charge belongs entirely to the four anchovy slices.
Dave ate the four anchovy slices, worth dollars, plus one plain slice worth dollar: he pays dollars.
Doug ate the other three plain slices: dollars.
Check: , the whole bill. The difference is .
The answer is .
Why this works
"Each paid for what he had eaten" means the cost of every slice is attached to the slice, including any extra charge for the topping on it. Pricing per slice first and then adding up each person's slices avoids all confusion; checking that the two payments sum to the total bill catches errors instantly.
Alternative approach
Work from the total: the bill is dollars. Doug's three plain slices are clearly dollars, so Dave owes the remaining , and the difference is .
The trap
Charging every slice the same 1.25 dollars (Dave 5 slices vs Doug 3 gives a 2.50 gap) or splitting the anchovy surcharge between both people.
Common mistakes
- Charging every slice the same dollars (Dave slices vs Doug gives a gap) or splitting the anchovy surcharge between both people.
- Forgetting Dave's extra plain slice, so Dave pays and Doug , a difference of (choice (B)).
Techniques
Set up the equation/formula and compute; no special trick needed