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Omni-MATH / Joey wrote a system of equations on a blackboard, where each of the equations…

Problem

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problem

Joey wrote a system of equations on a blackboard, where each of the equations was of the form a+b=ca+b=c or a⋅b=ca \cdot b=c for some variables or integers a,b,ca, b, c. Then Sean came to the board and erased all of the plus signs and multiplication signs, so that the board reads: $$\begin{array}{ll} x & z=15 \\ x & y=12 \\ x & x=36 \end{array}$$ If x,y,zx, y, z are integer solutions to the original system, find the sum of all possible values of 100x+10y+z100 x+10 y+z.
Plain-text mathematical notation (without MathML)
Joey wrote a system of equations on a blackboard, where each of the equations was of the form a+b=c or a⋅b=c for some variables or integers a,b,c. Then Sean came to the board and erased all of the plus signs and multiplication signs, so that the board reads: $$\begin{array}{ll} x & z=15 \\ x & y=12 \\ x & x=36 \end{array}$$ If x,y,z are integer solutions to the original system, find the sum of all possible values of 100x+10y+z.
Original LaTeX notation
Joey wrote a system of equations on a blackboard, where each of the equations was of the form $a+b=c$ or $a \cdot b=c$ for some variables or integers $a, b, c$. Then Sean came to the board and erased all of the plus signs and multiplication signs, so that the board reads: $$\begin{array}{ll} x & z=15 \\ x & y=12 \\ x & x=36 \end{array}$$ If $x, y, z$ are integer solutions to the original system, find the sum of all possible values of $100 x+10 y+z$.

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Source and history

task_id
769e8719-a76e-507e-b39f-c0b09c919f3d
task_key
test--769e8719-a76e-507e-b39f-c0b09c919f3d
task_revision_id
1
config / split
/ test

Official source

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