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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_2 / The weight of (1)/(3) of a large pizza together with 3(1)/(2) cups of orange slices is the same as the weight of (3)/(4) of a large pizza together with (1)/(2) cup of orange slices…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The weight of

\frac{1}{3}

of a large pizza together with

3 \frac{1}{2}

cups of orange slices is the same as the weight of

\frac{3}{4}

of a large pizza together with

\frac{1}{2}

cup of orange slices. A cup of orange slices weighs

\frac{1}{4}

of a pound. What is the weight, in pounds, of a large pizza? The answer can be written in the form

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. What is

m-n

Plain-text mathematical notation (without MathML)

The weight of (1)/(3) of a large pizza together with 3(1)/(2) cups of orange slices is the same as the weight of (3)/(4) of a large pizza together with (1)/(2) cup of orange slices. A cup of orange slices weighs (1)/(4) of a pound. What is the weight, in pounds, of a large pizza? The answer can be written in the form (m)/(n), where m and n are relatively prime positive integers. What is m−n?

Original LaTeX notation

The weight of $\frac{1}{3}$ of a large pizza together with $3 \frac{1}{2}$ cups of orange slices is the same as the weight of $\frac{3}{4}$ of a large pizza together with $\frac{1}{2}$ cup of orange slices. A cup of orange slices weighs $\frac{1}{4}$ of a pound. What is the weight, in pounds, of a large pizza? The answer can be written in the form $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m-n$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_2
task_id: 617fa2f8-5ebd-5add-a81c-6ad058e9065e
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f2
task_revision_id: 2
config / split: default / train

Official source

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