Answer the Following with Solutions:

Question

1. The sum of the digits of a two- digit number is 14. If the digits are reversed, the resulting number is 23 less than two times the original number. What is the original number?
2. A two -digit number is 6 more than the product of 7 and the sum of its digits. The number with the digits reversed is two more than the product of 3 and the sum of its digits. What is the number?

Answer 1

QUESTION 1:

We assume the two-digit number is xy. The number equals 10x+y.

If we reverse the digits, we will get yx. The new number equals 10y+x.

Because the new number is 23 less than two times the original number,

10y+x=2(10x+y)-23

We can simplify the above equation to get 8y-19x=-23 [1]

The sum of the digits of a two-digit number is 14. So x+y=14 [2]

If we solve this system of equations, we get x=5, y=9.

The original number is 59