 Mathematics
11 June, 15:45

# This is a popular type of problem that appeared in mathematics textbooks in the 1970s and 1980s. can you find the answer? the sum of the digits of a two-digit number is 6. if the digits are reversed, the difference between the new number and the original number is 18. find the original number.

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1. 11 June, 15:56
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A digit is a number in one of the places, so for example the number 54 has two digits; a tens place digit (5) and a ones place digit (4).

Say the mystery number is a two digit number = xy

* that's not x times y but two side by side digits.

Info given:

the sum of the digits of a two-digit number is 6

x + y = 6

if the digits are reversed, yx the difference between the new number and the original number is 18.

**To obtain the number from digits you must multiply by the place and add the digits up. (Example: 54 = 10 (5) + 1 (4))

Original number = 10x + y

Reversed/New number = 10y + x

Difference:

10y + x - (10x + y) = 18

9y - 9x = 18

9 (y - x) = 18

y - x = 18/9

y - x = 2

Now we have two equations in two variables

y - x = 2

x + y = 6

Re-write one in terms of one variable for substitution.

y = 2 + x

sub in to the other equation to combine them.

x + (2 + x) = 6

2x + 2 = 6

2x = 6 - 2

2x = 4

x = 2

That's the tens digit for the original number. Plug this value into either of the equations to obtain y, the ones digit.

2 + y = 6

y = 4

number "xy" = 24