Question

The sum of three numbers is 26. The second number is twice the first and the third number is 6 more than the second. What are the numbers??

Answer 1

4,8,14

Explanation:

Firstly, we should try to make an equation of this. Let's start off with the first number.

Because we have no clue what the first number is (for now), we can call it x.

Since we have no idea what the second number is (for now), but we do know that it's twice the first, we can call it 2x.

Since we aren't sure what the third number is either, we can call it 2x+6 (because it's the exact same number as the second number, just with six added to it).

Now, let's form our equation!

`x+2x+2x+6=26`.

We should first isolate the x to get...

`x+2x+2x=20` (I subtracted 6 on both sides).

Combine like terms...

`5x=20`

Divide both sides by 5...

`x=4`.

Now we can plug it into the equation!

First number is x, so `x=4`, therefore the first number is 4.

Second number is 2x and `x=4`, therefore `2(4)=8` so the second number is 8.

The last number is 2x+6 and `x=4`, so `2(4)+6=14`.

Just to double check...

14+8+4=26.

Therefore the answers are 4,8, and 16.

Answer 2

The three numbers are `4, 8 and 14`.

Explanation:

(i) Let the first number be `a`.

(ii) The second number is twice the first.

Second number = `2a`.

and

(iii) The third number is 6 more than the second.

So the third number is = `2a + 6`

The sum of three numbers is 26.

`therefore a+ 2a + (2a+6) = 26`

`=> a+ 2a + 2a+6 = 26`

`=> 5a+6 = 26`

`=> 5a = 26-6 = 20`

`=> a = 20/5 = 4`

`therefore a = 4`

So the three numbers are :
(i) `a=4`

(ii) `2a = 2\times 4 = 8` and

(iii) `2a+ 6 = 8+6 = 14`

The three numbers are `4, 8 and 14`.