Question

One number is 11 more than twice another number. If the sum of the numbers is twice their difference, find the numbers. List your answers in numerical order, separated by a comma.

Answer 1

Step-by-step explanation:

Let's say that the first number is A, and the second one is B

A is 11 more than twice of B

A = 11 + 2B ... (1)

.

The sum of the numbers (A + B) is twice their difference (A - B)

A + B = 2(A-B)

A + B = 2A - 2B

A - 3B = 0 ... (2)

.

Substituting (1) into (2):

11 + 2B - 3B = 0

11 - B = 0 -> B = 11

.

Then, insert the value of B into either (1) or (2) (I'm using (1) here):

A = 11 + 2B = 11 + 2*11 = 11 + 22

A = 33