pizza coupon

Question

If you have a coupon for 2 medium pizza's for $12.99 and a large pizza for $10.99.  Which is the better deal?

Answer 1

Assuming that you are only concerned about the size of the pizzas and the cost.

size of Medium Pizza = πr_m²

size of Large Pizza = πr_l²

 

Set up the equation to determine when the two options provide identical values.  This will allow you to test, based on the comparison of the relative sizes, which is the better deal.

 

2πr_m²/$10.99 = πr_l²/$12.99

factor out pi

 

2r_m²/$10.99 = r_l²/$12.99

multiply both sides by $12.99

 

2r_m² ($12.99)/$10.99 = r_l²

Multiply together the numbers on the left hand side (truncate the answer to four significant digits).

 

2.364 r_m² = r_l²

divide both sides by r_m²

 

2.364 = r_l²/r_m²

 

take the square root of both sides

 

1.538 = r_l/r_m

 

Pizza parlors generally advertise the size of their pies by diameter of the pies, but since a diameter = 2 x radius, the ratio is the same.

 

so, if the diameter of the Large pie is 1.538 times greater than the medium pair, the large pie is the better deal.  If the ratio of diameter of large to diameter of Medium is less than 1.538, the Medium is the better deal.