Question 713290: The sum of the digits of a two-digit number is 10. The value of the number is 16 times the units' digit. Find the number.
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! X is the amount of tens, and Y is the amount of ones.
The number is 10X+Y.
Given information indicates these:
X+Y=10 and 10X+Y=16Y
Those are a system of two equations and two unknown variables. Working with the second one,
10X-16Y+Y=0
10X-15Y=0
2X-3Y=0, simpler version of the second equation.
Simpler system to solve is
X+Y=10
2X-3Y=0
Multiplying first one by 3 and then adding both equations:
3X+3Y=30
2X-3Y=0
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5X+0=30
X=6, this means Y=4.
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