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Sonny Kuphal

Lvl 10
3y ago
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12y ago

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.)

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