Question

3) Find two consecutive even integers such that their sum is equal to the difference of 3 times the larger & 2 times the smaller.

What do they mean by the larger and the smaller?

Answer 1

In assumption, x is the smaller even integer and x+2 is the next so it will be larger.

The integers are 4 and 6

Explanation:

Let the two consecutive even integers be x and x+2

Here x is the smaller even integer and x+2 is the next so it will be larger.

Now according to the given statement

Sum of both:
`x+x+2`

difference of 3 times the larger & 2 times the smaller:
`3(x+2)-2x`

Putting the sum and difference equal:

`x+x+2 = 3(x+2)-2x`

Solving the equation

`2x+2 = 3x+6-2x\\2x+2 = x+6\\2x+2-x = x+6-x\\x+2 = 6\\x+2-2 = 6-2\\x = 4`

The next integer will be:

`x+2 = 4+2 = 6`

Hence,

In assumption, x is the smaller even integer and x+2 is the next so it will be larger.

The integers are 4 and 6.