What two numbers multiply to 140 and add up to 31?

Answer 1

171

Answer 2

Oh, what a delightful math puzzle we have here! Let's see, the two numbers we're looking for are 20 and 7. When you multiply them, you get 140, and when you add them together, you get 27. Keep exploring those numbers and remember, there are always happy little solutions waiting to be discovered.

Answer 3

Let's denote the two numbers as x and y. We know that xy = 140 and x + y = 31. By solving these two equations simultaneously, we can find that the two numbers are 20 and 7. This is because 20 * 7 = 140 and 20 + 7 = 27.

Answer 4

Well, well, well, aren't we playing Sherlock Holmes today? The two numbers you're looking for are 20 and 7. They multiply to 140 and add up to 27, just like you wanted. Hope that tickles your fancy, detective!

Answer 5

If we call the two numbers a and b then ab = 140 and a + b = 31. Solving the second equation for b results in b = 31 - a. Then substituting this back into the first equation results in:

a(31 - a) = 140

Distribute and subtract 31 from both sides:

-a2 + 31a - 140 = 0

Use the quadratic formula to solve for a:

a = about 5.488 or 25.516

Then plug this numbers back into an original equation (such as a + b = 31) and solve for b. If a is 5.488 then b ends up being 25.516. If a is 25.516 then b ends up being 5.488.

So the two numbers are about 5.488 and 25.516. (The exact forms are (1/2)(31 - sqr(401)) and (1/2)(31 + sqr(401)) The plus or minus in the quadratic formula takes care of what both numbers will be, so you don't have to substitute back if you find both possible values for a.)