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Question 522973: the difference of digits of two digit number is 1.five times the sum of the number plus one is equal to the number. find the number
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! the difference of digits of two digit number is 1.
five times the sum of the number plus one is equal to the number.
find the number
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Two digits, a, b
then
10a + b = the number
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"the difference of digits of two digit number is 1."
a - b = 1
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"five times the sum of the number plus one is equal to the number."
5(a+b) + 1 = 10a + b
5a + 5b + 1 = 10a + b
5a - 10a + 5b - b = -1
-5a + 4b = -1
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Use substitution here, multiply the 1st equation by 4, add to the 2nd eq
+4a - 4b = 4
-5a + 4b = -1
--------------addition eliminates b, find a
-a = 3
a = -3
find b
-3 - b = 1
-b = 1 + 3
-b = 4
b = -4
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The number
-3(10) + (-4) = -34 is the number
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Usually not a neg answer in these problems, see if this works in the statement:
"five times the sum of the number plus one is equal to the number."
5(-3 + (-4)) + 1 = -34
5(-7) + 1 = -34
-35 + 1 = -34; confirms our solution of -34
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