# The sum of two numbers is 20. The larger number is four less than twice the smaller number. What are the two numbers?

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Assume that the numbers are x and y.

==> x+y=20....(1)

x=2y-4

Substitute with x=2y-4 in equation(1):

(2y-4)+y=20

3y-4 =20

ADD 4:

3y=24

Divide by 3:

y=24/3=8

==> x=2(8)-4 = 12

To check:\

12+8 = 20

12= 2(8)-4 =12

let x be the larger of the two numbers, and y be the other number.

Then:

x + y = 20 ... (1)

and

x = 2y - 4

Shifting the term 2y in above equation from right to left hand side we get:

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

Subtracting equation (2) from equation (1) we get:

x - x + y + 2y = 20 + 4

3y = 24

Therefore:

y = 24/3 = 8

Substituting this value of y in equation (1) we get:

x + 8 = 20

x = 20 - 8 = 12

Answer:

Two numbers are 12 and 8.

Let x be the bigger number and let y be the smaller number.

x + y = 20

x = 2y -4

So now we substitute this value of x into the original equation.

2y - 4 + y = 20

3y - 4 = 20

3y = 24

y = 8

If y = 8, then

x = 12

because x + y must equal 20. To check this, let us see if these values work with the other equation

12 = (2*8) - 4

12 = 16 - 4

True -- so this is correct.

Let the smaller number be x.

Then the larger number is 4 times x = 4x.

The sum of the two numbers = x+4x= 5x but this is given to be 20. So 5x = 20. Therefore, x = 20/5 = 4 is the smaller number. The larger number 4x , therefore, is 4*4 = 20