Two Digit + Sum of digits

Algebra Level 1

I've chosen a two digit number such that when I add it to the sum of its digits, the result is 50. What is my two digit number?

The answer is 43.

3 solutions

Swarang Pundlik
Oct 17, 2015

the number plus sum of its digits meaning 11 x +2 y = 50. also both x and y are single digit numbers. therefore x + y is less than or equal to 18. solving for x gives x more than or equal to 4. putting x = 4 in the previous equation gives y = 3. hence the number is 43

Why are you guy using 11 and 2 here? Where do they come from? Plz explain for me. Tks

Teo Smith - 5 years, 8 months ago

1st digit = x

2nd digit = y

the original number = 10x + y

the sum of its digits = x + y

the sum of its digits + original number = 11x + 2y

Victor Chen - 5 years, 8 months ago

without loss of generality, consider digit at ten's place be x and at unit's place be y. rest is face value place value game. 4th grade maths

Swarang Pundlik - 5 years, 8 months ago

10x+y = the number in question (multiply x by 10 because it is in the 10s column). 10x+y (+x+y) > adding the number in question plus the digits of the number.

11x+2y = 50. x must be less than 5. If you solve for y assuming x is 1, 2, 3, or 4 there is only one solution. I could not come up with a way to solve for x without making assumptions which were X had to be an even number for the solution to be divisible by 2 to be a whole number so X had to be 2 or 4. 2 was too small a number to sum to 50.

Donna Kat - 5 years, 7 months ago

Brian Daniels
Oct 15, 2015

Just had to think about it. At first I thought 30-something, like 39, but it didn't work. 39 + 3 + 9 = 51

BUT 43 + 4 + 3 = 50

I was honestly hoping it would be 42, lol.

suppose the 2 digit number be 10x+y. so the problem goes as 10x+y+x+y=50 11x+2y=50. now x and y must be integers and single digit. so they must be 4 and 3.

Bikash Kumar - 5 years, 8 months ago

Wisnu Ops
Oct 18, 2015

If the number can be written as $ab$ ( $a$ is the tens and $b$ is the units), then the number is $10a + b$ , and the sum of its digits is $a+b$ .

So the number plus the sum of its digits equals to $11a+2b = 50$ . Since $a$ and $b$ are integers between $1$ and $9$ (inclusive), therefore the only possible solution is:

$a = 4$
$b = 3$

So, the number is $43$ .

Two Digit + Sum of digits

The answer is 43.

3 solutions

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