Question

Two numbers less than 100 are composed of the same digits, but are in reverse order. If their sum is 110 and difference is 18, find the numbers. The sum of four consecutive even numbers is 92, find the numbers.​

Answer 1

First part: 64 and 46
Second part, 10, 12, 14, 16.

Explanation:

First number has his first digit A, and second digit B, ie it can be written as 10A+B. Second number becomes then 10B+A.

Add them together, the sum becomes 11A + 11B = 110. (or A+B = 10 by dividing by 11).

Subtract them from each other, and you get 9A-9B = 18 (or dividing by 9 A-B=2)

At this point it's easy to find the solution A=6, B=4 which makes the two numbers 64 and 46.

Callthe first number of the chain 2x, the second 2x+2, third is 2x+4, fourth is 2x+6. Add them together, you get 8x +2+4+6= 8x+ 12=92 which easily solves for x = 10 and the four numbers are 10, 12, 14, 16.