Find two consecutive even numbers such that the sum of 3 times the smaller and 5 times thelarger is106.

The two consecutive even numbers such that the sum of three times the smaller and five times the larger is 106 are 12 and 14, computed using the linear equation in one variable 3x + 5(x + 2) = 106.

We are given two consecutive even numbers, thus the larger number will be two more than the smaller one, as consecutive even numbers differ by two.

We assume the smaller number to be x.

Thus, the larger number = x + 2.

We have been given that three times the smaller number summed with five times the larger number results in 106.

This can be shown by the linear equation in one variable:

3x + 5(x + 2) = 106.

To find the numbers, we need to solve this linear equation in one variable as follows:

3x + 5(x + 2) = 106,

or 3x + 5x + 10 = 106 {Simplifying},

or, 8x + 10 = 106 {Simplifying},

or, 8x + 10 - 10 = 106 - 10 {Subtracting 10 from both sides of the equation},

or, 8x = 96 {Simplifying},

or, 8x/8 = 96/8 {Dividing both sides of the equation by 8},

or, x = 12 {Simplifying}.

Thus the smaller number, x = 12.

The larger number, x + 2 = 12 + 2 = 14.

Thus, the two consecutive even numbers such that the sum of three times the smaller and five times the larger is 106 are 12 and 14, computed using the linear equation in one variable 3x + 5(x + 2) = 106.

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