One number is 6 more than 2 times another. Their product is 6 more than 2 times their sum. Find the numbers.

Answer 1

Two number A and B.

A = 2B + 6

AB = 2(A+B) + 6

Substitute A into the 2nd equation:

(2B+6)B = 2(2B+6 + B) + 6

12B^2 + 6B = 4B^2 + 2B + 18

A = 1.271 and -1.771

B = 27

Answer 2

Hi Star!

Here is my answer. Make sure you check out the graph at the end!

Let me know if you need any additional help! :)

Thanks

Bob

Answer 3

For this problem, I think the best way to approach it is to write equations using numbers from the words you are given. This makes it easier to visualize what they are asking. Let's say that the first number is x and the second number is y. Therefore, "one number" is x, "6 more than" means add 6, and "2 times another" means 2 times y, or:

x = 6 + 2y

For the next sentence, "their product" is x*y and "6 more than" is again adding 6, and "2 times their sum" is 2(x+y) or:

xy = 6 + 2(x + y)

Now, you can use the first equation, which is solved for x and plug it into all the times you see x in the second equation to get:

(6 + 2y) = 6 + 2 ((6+ 2y) + y)

Now, simplify the equation and isolate the variable y:

6 + 2y = 6 + 2 (6 + 3y)

6+ 2y = 6 + 12 + 6y

6 + 2y = 18 + 6y

-12 = 4y

y = -3

Then, plug this value for y back into the equation for x to get

x = 6 + 2y

x = 6 + 2(-3)

x = 6 - 6

x = 0

To check your answer, you can plug both the x and y value back into the two equations you wrote and make sure they are both equal.