2023 AMC 12A Problems/Problem 2
- The following problem is from both the 2023 AMC 10A #2 and 2023 AMC 12A #2, so both problems redirect to this page.
Contents
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 (Substitution)
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 by the given gives
~ItsMeNoobieboy ~walmartbrian
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
where is the pizza weight and is the weight of cup of oranges Since oranges weigh pound per cup, the oranges on the LHS weigh cups x pounds/cup = pound, and those on the RHS weigh cup x pounds/cup = pound.
So + pound = + pound; + pound = .
Multiplying both sides by , we have ; ; = weight of a large pizza = pounds = pounds.
~Dilip ~ by A_MatheMagician
Video Solution (🚀 Just 1 min 🚀)
~Education, the Study of Everything
Video Solution by Math-X (First understand the problem!!!)
https://youtu.be/cMgngeSmFCY?si=ULlMU09VdlpsRW3n&t=205
Video Solution by CosineMethod [🔥Fast and Easy🔥]
https://www.youtube.com/watch?v=CpboCxGBcWY
Video Solution
~Steven Chen (Professor Chen Education Palace, www.professorchenedu.com)
Video Solution (easy to digest) by Power Solve
https://www.youtube.com/watch?v=8huvzWTtgaU
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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