Use the three steps to solve the problem. one number is 11 more than twice another number. if the sum of the numbers is twice their difference, find the numbers.

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

One number is 11 more than twice another number. Thus,

x = 2y + 11

The sum of the numbers is twice their difference, thus,

x + y = 2(x-y), which simplifies to:

x + y = 2x - 2y

3y = x  (Now plug this back to the first equation:

3y = 2y + 11, and solve:

y = 11

Plug in y = 11 to the first equation:

x = 2(11) + 11 = 22 + 11 = 33

Thus the numbers are: x = 33, y = 11.

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