Question

What times what equals 30 but add to get 40?

Answer 1

Lets call those two unknown numbers a, b and write the info in the problem as equations:
a*b = 30
a + b = 40
lets solve for a in the second equation and substitute in the first:
a + b = 40
a = 40 - b
therefore:
a*b = 30
(40 - b)b = 30
40b - b^2 = 30
b^2 - 40b + 30 = 0
if we apply the general quadratic equation to solve we have:
b = (40 +- √(1600 - 120))/2
b = (40 +- √(1480))/2
b = (40 +- 38.47)/2
There are two solutions:
b1 = (40 + 38.47)/2
b1 = 39.24
b2 = (40 - 38.47)/2
b2 = 0.765
lets use the second solution b2 = 0.765, and substitute in the first equation to find a:
a*b = 30
a*0.765 = 30
a = 30/0.765
a = 39.216
so the numbers are 39.216 and 0.765

Answer 2

(15x2) = 30, (30 + 10) = 40 .. (P.E.M.D.A.S)