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Omni-MATH / Let n be the answer to this problem. Box B initially contains n balls, and Box A contains half as many balls as Box B. After 80 balls are moved from Box A to Box B, the ratio of ba…

Problem

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

problem

Let nn be the answer to this problem. Box BB initially contains nn balls, and Box AA contains half as many balls as Box BB. After 80 balls are moved from Box AA to Box BB, the ratio of balls in Box AA to Box BB is now pq\frac{p}{q}, where p,qp, q are positive integers with gcd(p,q)=1\operatorname{gcd}(p, q)=1. Find 100p+q100p+q.
Plain-text mathematical notation (without MathML)
Let n be the answer to this problem. Box B initially contains n balls, and Box A contains half as many balls as Box B. After 80 balls are moved from Box A to Box B, the ratio of balls in Box A to Box B is now (p)/(q), where p,q are positive integers with gcd(p,q)=1. Find 100p+q.
Original LaTeX notation
Let $n$ be the answer to this problem. Box $B$ initially contains $n$ balls, and Box $A$ contains half as many balls as Box $B$. After 80 balls are moved from Box $A$ to Box $B$, the ratio of balls in Box $A$ to Box $B$ is now $\frac{p}{q}$, where $p, q$ are positive integers with $\operatorname{gcd}(p, q)=1$. Find $100p+q$.

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Source and history

task_id
b02b974f-50d6-54bb-97ea-a5fca94879b6
task_key
test--b02b974f-50d6-54bb-97ea-a5fca94879b6
task_revision_id
1
config / split
/ test

Official source

initial import