Algebraic Expressions

Let the smallest odd number be . Then, the three consecutive odd numbers will be . The sum of the three consecutive odd numbers is:

x + (x + 2) + (x + 4) = 3x + 6

Let the smallest even number be . Then, the four consecutive even numbers will be . The sum of the four consecutive even numbers is:

y + (y + 2) + (y + 4) + (y + 6) = 4y + 12

We are told that the sum of the four consecutive even numbers is 107 more than the sum of the three consecutive odd numbers. Therefore, we can write the equation:

4y + 12 = (3x + 6) + 107

Simplifying:

4y + 12 = 3x + 113
4y = 3x + 101 {(Equation 1)}

We are also told that the sum of the smallest odd number and the smallest even number is 55. Therefore:

x + y = 55 {(Equation 2)}

Now, solve these two equations simultaneously. From Equation 2:

y = 55 - x

Substitute this into Equation 1:

4(55 - x) = 3x + 101
220 - 4x = 3x + 101
220 - 101 = 3x + 4x
119 = 7x
x = 119 / 7 = 17

Substitute into Equation 2:

17 + y = 55
y = 55 - 17 = 38

Thus, the smallest even number is .