SOLUTION: How do I solve using two equations with two variables?
The sum of the digits of a two-digit number is 11. If 27 is added to the number, the digits will be reversed. Find the n
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The sum of the digits of a two-digit number is 11. If 27 is added to the number, the digits will be reversed. Find the n
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Question 141497This question is from textbook Prentice hall algebra 1
: How do I solve using two equations with two variables?
The sum of the digits of a two-digit number is 11. If 27 is added to the number, the digits will be reversed. Find the number. This question is from textbook Prentice hall algebra 1
You can put this solution on YOUR website! Let x = the 10's digit
Let y = the units digit
:
10x + y = "the number"
:
Just write an equation for what it says:
:
"The sum of the digits of a two-digit number is 11."
x + y = 11
y = (11-y); use for substitution
:
"If 27 is added to the number, the digits will be reversed."
10x + y + 27 = 10y + x
:
10x - x + 27 = 10y - y
:
9x + 27 = 9y
;
Simplify, divide equation by 9
x + 3 = y
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Find the number.
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Substitute (11-x) for y in the above equation:
x + 3 = 11 - x
:
x + x = 11 - 3
:
2x = 8
x =
x = 4
Then
y = 11 - y
y = 7
:
Our number: 47
:
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Check solution in the statement:
"If 27 is added to the number, the digits will be reversed."
47 + 27 = 74; confirms our solutions
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did this make sense to you, not that hard, right?
