```Question 214932
I need your help with this digit problem: The sum of the digits of a two-digit number is 12. The value of the number is two more than 11 times tens digit. Find the number.
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x = first digit
y = second digit
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The sum of the digits of a two-digit number is 12.
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this means that x + y = 12
x is the tens digit.
y is the units digit.
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The value of the number is two more than 11 times tens digit.
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10 * x + y is the value of the number.
11 * x + 2 is two more than the value of the tens digit * 11.
10*x + y = 11*x + 2
This says that the value of your number (10*x + y) is 2 more than 11 times the tens digit (11*x + 2)
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You have 2 equations that need to be solved simultaneously.
They are:
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x + y = 12
and
10*x + y = 11*x + 2
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You can solve for y in your second equation of 10*x + y = 11*x + 2 to get:
y = x + 2
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You can substitute for y in your first equation to get:
x + (x + 2) = 12
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Remove parentheses to get:
2x + 2 = 12
Solve for x to get:
x = 5
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If x = 5, then x + y = 12 becomes:
5 + y = 12
Solve for y to get:
y = 7
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You have:
x = 5
y = 7
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Sum of the digits is 12 which is good.
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The number is xy = 57
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The value of the number is 2 more than 11 times the tens digit.
11 * the tens digit is 11 * 5 = 55
55 + 2 = 57
This is true confirming the values for x and y are good.
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