Algebraic puzzles

Question

What is the sum of four times a number and twice the sum of the same number and three

Answer 1

Since this is a word problem, it can be helpful to separate the components visually. "And" indicates addition, so any place we see "and", we'll put "+". "Times" indicates multiplication, so any place we see "times", we'll put *. Any place we see a number value, we'll put that number. The word "twice" means multiplication by 2, or "two times." Since we do not know the value of "some number," it is a variable.

Let n = "some number."

Then we have:

4*n + 2*(n + 3)

We then multiply through the parentheses:

= 4*n + 2*n + 2*3

= 4n + 2n + 6

All we can do from here is add like-terms:

= 6n + 6

The tricky part of this question is noticing that the question asks for twice the sum of "some number" and 3, which means 2 * the entire unit of ("some number" + 3). If we only multiply "some number" by 2, we will end up with 6n + 3, which is incorrect.

Answer 2

Work these problems a little at a time.......

What is the sum of four times a number and twice the sum of the same number and three

Number = 4(x) + 2( x + 3)

You kind of go along the sentence, and copy down below it what it says... (I hope this makes sense to you with the above example).

= 4x + 2x + 6 (after you distribute the 2, multiplying both the x and then the 3 by 2)

= 6x + 6 (gather like terms, this is the answer to the problem).

For the proof, choose ANY integer number and put it in: Let's choose 11, then -3, then zero for the proof!

6(11) + 6 = 4(11) + 2(11+3)

72 = 44 + 2(13) = 72 check 72=72 for x =11

6(-3) + 6 = 4(-3) + 2(-3+3)

-12 = -12 + 0 check! -12 = -12

6(0) + 6 = 4(0) + 2(0+3)

6 = 2(3) = 6 check! 6 = 6

I hope this helps you!