# Find two numbers such that their sum is 31 and one of then is four more than twice the other

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The numbers are 2 and 29. Here is how we find this answer:

We can set up 2 equations here:

x + y = 31

x = 2y +4

Using the first equation to find for y, we see that y = 31 - x.

So now we substitute

x = 2 (31 - x) + 4

x = 62 - 2x + 4

3x = 66

x = 22

If x = 22, then y = 9

To check, let us use these values in the other equation. We know that

x = 2y + 4

So we ask, does

22 = (2*9) + 4

We find that 22 does equal 18 + 4 so we have the right answer.

Let us assume that the numbers are x and y

Then x+y =31.....(1)

One of them is four more that twice the other

This could be translated as :

x = 4+ 2y .....(2)

Now substitute in (1)

x+y =31

(4+2y) + y =31

4 + 3y= 31

3y = 31-4 = 27

y= 27/3 = 9

x= 4+2y = 4+ 2(9) = 4+ 18 = 22

To check:

x+y = 31

22+ 9 = 31

31=31

And :

x= 4+ 2y

22= 4+ 2(9)

22= 4+ 18

22= 22

Then the numbers are 9 and 22

We assume x and 31-x are the two numbers whose sum is obviously 30.

By the 2nd codtion, x = 4 more thant twice (31-x). Or

x = 4+2(31-x).

x= 4+62-2x.

3x = 66.

x= 66/3 =22. The other number =31-x = 31-22 = 9

So 22 and 9 are the numbers. Which checks 22 = 4+2(9).

Let's note the number a and b.

Their sum is 31:

a+b = 31

Let's put the number "a" as being smaller number, so the number "b" is:

b = 4 +2a

Now, we'll substitute "b" by it's expression, into the first expression:

a+4 +2a= 31

3a + 4 = 31

We'll subtract 4 both sides:

3a = 31-4

3a = 27

We'll divide by 3:

**a = 9**

But b = 4 +2a, so b = b = 4 +2*9

b = 4 + 18

**b = 22**

Let:

x = smaller of the number

y = the other number.

Then as per the conditions given:

x + y = 31 ... (1)

And:

y = 2x + 4

2x - y = -4 ... (2)

Adding equations (10 and (2):

x + 2x + y - y = 31 - 4

3x = 27

x = 27/3 = 9

Substituting the value of x in equation (1):

9 + y = 31

y = 31 - 9 = 22

Answer:

The two numbers are 9 and 22.