Question

Sum of four consecutive even numbers is 49 more than sum of three consecutive odd numbers and sum of lowest oddand lowest even number is23 find the largest even number

Answer 1

Let the lowest even number be x
the lowest odd number = 23-x (this is because the sum of the lowest even no. and the lowest odd no =  23)

The four consecutive even numbers are:
x, x+2, x+4 and x+6

their sum =  x+x+2+x+4+x+6 = 4x+12

the three consecutive odd numbers are
23-x, 21-x, 19-x. (they differ by 2)
their sum = 23-x+21-x+19-x= 63-3x

The sum of the four consecutive even numbers is 49 more than the sum of 3 consecutive odd numbers, this can be written as:

4x+12 - (63-3x) = 49
4x+12 - 63 + 3x = 49

7x - 51 = 49
7x = 100
x = 100/7

the largest even number = x+6 = 100/7 + 6 = 142/7

Since we are getting fractional values, it means this problem has not solution. Fractions can not be even or odd.