2001 AMC 10 Problem 3

Problem 3 of 25EasierAlgebra

The sum of two numbers is

S.

Suppose

3

is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?

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Solution

Let the numbers be

a

and

b,

a+b=S.

After adding

3

to each and doubling, the sum is

2(a+3)

+2(b+3)

=2(a+b)+12

=2S+12.

Thus, the correct answer is E.

Concepts: algebraic manipulation · distributive property

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.