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MATH / If A, B, and C represent three distinct digits from 1 to 9 and they satisfy the following equations, what is the value of the sum A+B+C? (In the equation below, AA represents a two…

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problem

If AA, BB, and CC represent three distinct digits from 1 to 9 and they satisfy the following equations, what is the value of the sum A+B+CA+B+C? (In the equation below, AAAA represents a two-digit number both of whose digits are AA.) A+B=CA+B=CAA−B=2×CAA-B=2\times CC×B=AA+AC\times B=AA+A
Plain-text mathematical notation (without MathML)
If A, B, and C represent three distinct digits from 1 to 9 and they satisfy the following equations, what is the value of the sum A+B+C? (In the equation below, AA represents a two-digit number both of whose digits are A.) A+B=CAA−B=2×CC×B=AA+A
Original LaTeX notation
If $A$, $B$, and $C$ represent three distinct digits from 1 to 9 and they satisfy the following equations, what is the value of the sum $A+B+C$? (In the equation below, $AA$ represents a two-digit number both of whose digits are $A$.) $$A+B=C$$$$AA-B=2\times C$$$$C\times B=AA+A$$

level

Level 4

type

Number Theory

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Source and history

task_id
053f6e4f-1a0d-5feb-bd03-f692a265e099
task_key
number~5ftheory--test--053f6e4f-1a0d-5feb-bd03-f692a265e099
task_revision_id
1
config / split
number_theory / test

Official source

initial import