Important Math Question

[Boomwebsearch]

What adds to be the bottom number but also multiplies to be the top (view the attachment) ?   I am asking this off-topic question to see if anyone knows the answer and can help me by letting me know. I am trying to review some mathematics concepts that I learned a long time ago. 

[NinJake]

8 and 6

[Boomwebsearch]

3 minutes ago, NinJake said:

8 and 6

Thank you for submitting your response which has successfully solved my question.

[Guest]

He got that by listing all numbers that multiply to 48, and then seeing which 2 add up to 14. 

[NinJake]

Just now, fpo said:

He got that by listing all numbers that multiply to 48, and then seeing which 2 add up to 14. 

Or you could do it in reverse by saying what adds to 14 and testing those 2 numbers. 13 and1, 12 and 2, 11 and 3, 10 and 4, 9 and 5, 8 and 6, 7 and 7. Those are all the possibilities.

[Megah3rtz]

27 minutes ago, NinJake said:

Or you could do it in reverse by saying what adds to 14 and testing those 2 numbers. 13 and1, 12 and 2, 11 and 3, 10 and 4, 9 and 5, 8 and 6, 7 and 7. Those are all the possibilities.

Probably faster to do it that way.

[Dash Lambda]

The way to do it without just testing possibilities is with a system.

 

ab = 48

a + b = 14

 

a(14 - a) = 48  ⇒  a² - 14a + 48 = 0

a = 7 ± 1

[Purush_10]

We have this property of number system that for given sum of two numbers say a+b = c, the maximum product possible i.e. ab from the different possible combinations of a and b  will be when a = b = (c/2)

In this case the sum is 14 and so the combinations of a and b can be (13,1), (12,2), (11,3), (10,4), (9,5), (8,6), (7,7)
Now if we see the products of all the combinations we get:
13*1 = 13, 12*2 = 24, 11*3 = 33, 10*4 = 40, 9*5 = 45, 8*6 = 48, 7*7 = 49 
Now the reason I mentioned this is that in this case we have a pretty small number 14, but in case it was a relatively bigger number it would be time-taking to go through the products of all possible combinations. In such cases, you can try figuring out the maximum product possible and then judge how much the required product (48 in this case) differs from this maximum value (49 in this case). Then you can approximate which combination you can consider next because if you look closely, the products are in ascending order. It would be easier and faster I believe.