2023 AMC 12A Problems/Problem 2
Contents
[hide]Problem
The weight of of a large pizza together with cups of orange slices is the same as the weight of of a large pizza together with cup of orange slices. A cup of orange slices weighs of a pound. What is the weight, in pounds, of a large pizza?
Solution 1
Use a system of equations. Let be the weight of a pizza and be the weight of a cup of orange slices. We have Rearranging, we get Plugging in pounds for gives
~ItsMeNoobieboy
Solution 2
Let: be the weight of a pizza. be the weight of a cup of orange.
From the problem, we know that .
Write the equation below:
Solving for :
~d_code
Solution 3
P/3 + 7/2 R = 3/4 P + R/2 where P = pizza weight and R = weight of cup of oranges
Since oranges weigh 1/4 pound per cup, the oranges on the LHS weigh 7/2 cups x 1/4 pounds/cup = 7/8 pound, and those on the RHS weigh 1/2 cup x 1/4 pounds/cup = 1/8 pound.
So P/3 + 7/8 pound = 3/4 P + 1/8 pound; P/3 + 3/4 pound = 3/4 P.
Multiplying both sides by LCM (3,4) = 12, we have 4P + 9# = 9P; 5P = 9#; P = weight of a large pizza = 9/5 pounds = pounds.
~Dilip
See Also
2023 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
2023 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 1 |
Followed by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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