# Thread: Solving using simultaneous equations?

1. ## Solving using simultaneous equations?

Good day everyone. I have a big conundrum here and I urgently need your help:
A two-digit number is equal to 4 times the sum of its digits. If the digits of the number are reversed, the new number formed is 27 more than the original number. Find the original number.
There is a solution that starts with this:
Let $x$be tens digit and $y$ be the units digit of the original number.
Original number is $10x+y$ and the sum of its digits is $x+y$.
Number formed by reversing its digits = $10y+x$.

I can comprehend what it's trying to elucidate on, however, I still do not know

• what is the meaning of the units digit
• what is the purpose of having a 10 in the algebraic expressions $10x +y$ and $10y+x$

Can you please help me explain? Thank you so much!

2. Originally Posted by PythagorasNeophyte
Good day everyone. I have a big conundrum here and I urgently need your help:

There is a solution that starts with this:
Let $x$be tens digit and $y$ be the units digit of the original number.
Original number is $10x+y$ and the sum of its digits is $x+y$.
Number formed by reversing its digits = $10y+x$.

I can comprehend what it's trying to elucidate on, however, I still do not know

• what is the meaning of the units digit
• what is the purpose of having a 10 in the algebraic expressions $10x +y$ and $10y+x$

Can you please help me explain? Thank you so much!
Take 13 for example, 3 is the unit digit and 1 is the tenth digit.

13 = (10 x 1) + 3

For 3 digits number (call the digits xyz), the expression for this number would be

100x + 10y + z