Question

The difference between the digits of a two-digit number is 1. The number itself is one more than five times the sum of its digits. If the unit digit is greater than the tens digit, find the number

Answer 1

The number is → 56

Explanation:

tens digit
`\Rightarrow x`

unit digit
`\Rightarrow y`

"The difference between the digits of a two-digit number is 1...", " ...the unit digit is greater than the tens digit..."

`y-x=1 \qquad \textbf{ec.1}`

"The number itself is one more (unit) than five times the sum of its digits..."

`10x+y=5(x+y)+1\\ 10x+y= 5x + 5y+1\\5x= 4y+1 \qquad \textbf{ec.2}`

we clear "y" in equation 1:

`y=1+x \qquad \textbf{ec.3}`

then we substitute in equation 2:

`5x=4(1+x)+1\\5x=5+4x\\\boxed{x=5}`

Finally, we substitute in equation 3:

`y=1+5\\\boxed{y=6}`

With this we have solved the exercise.

`\text{-B$\mathfrak{randon}$VN}`