algebra mathematical ability test

Question

I am a two -digit number. My tens digit is greater than my units by 3 .If you add my digits, the sum is one more than twice the difference of my digits.What number am I?

Answer 1

Hi, Sarah.

Okay, so let's call the two-digit number XY. Where X is the 10's place and Y is in the 1's place.

IF the tens digit is great than the ones digit by 3 then:

X = Y + 3

Also, since the sum of the digits is 1 more than twice the difference of the digits then:

X + Y = 2(X - Y) +1

Now, substitute Y + 3 for X in the 2nd equation.

(Y + 3) + Y = 2 ((Y + 3) - Y) + 1

2Y + 3 = 2(3) + 1

2Y = 7 - 3 = 4

Y = 2

Now substitute Y = 2 into X = Y + 3:

X = 2 + 3 = 5

So, XY = 52.

Now, check.

IS the tens digit (5) greater than the ones digit(2) by 3? Yes 5 - 2 = 3.

Is the sum of the digits 5+2 = 7, one more than twice the difference? 2(5-2) + 1 = 6+ 1 + 7.

Yes.

Therefore, the answer 52 is correct.