SOLUTION: The sum of the digits of a two-digit number is 8. If 16 is added to the original number, the result is 3 times the original number with its digits reversed, Find the original num
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Question 121861This question is from textbook
: The sum of the digits of a two-digit number is 8. If 16 is added to the original number, the result is 3 times the original number with its digits reversed, Find the original number. This question is from textbook
You can put this solution on YOUR website! Write an equation for each statement:
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Let the original number = 10x + y
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The sum of the digits of a two-digit number is 8.
x + y = 8
or
x = (8-y); use for substitution
:
"If 16 is added to the original number, the result is 3 times the original number with its digits reversed,"
(10x + y) + 16 = 3(10y + x)
10x + y + 16 = 30y + 3x
10x - 3x = 30y - y - 16
7x = 29y - 16
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Find the original number.
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Substitute (8-y) for x in the above equation:
7(8-y) = 29y - 16
56 - 7y = 29y - 16
56 + 16 = 29y + 7y
72 = 36y
y =
y = 2 is the units digit
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Find x:
8 - 2 = 6 is the 10's digit
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Our original number is 62
:
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Check solution in the statement:
"If 16 is added to the original number, the result is 3 times the original number with its digits reversed,"
62 + 16 = 3(26)
78 = 78; confirms our solution
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How about this. Did it make it understandable? Could you do a similar problem now?
