a number consists of two digits such that the square of the digit in the tens place exceeds the unit place digit by 1. If the number is 18 more than the sum of digits. Find the number.
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Establish the variables
x = tens place
y = ones place
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Given
x = y+3
x+y = (10x+y)
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Substitute x into the equation
y+3 + y = (10(y+3) + y)
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Distribute the 10
2y + 3 = (10y + 30 + y)
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Combine like terms
2y + 3 = (11y + 30)
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Multiply both sides by 7 to be rid of the fraction
14y + 21 = 11y + 30
Isolate y
14y - 11y = 30 - 21
3y = 9
y =9
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x = y+3 = 3+3
x=6
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Then number is 63
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