What numbers that when you add it equals to30 but when you divided it by the smaller number the result is the smaller number?

Answer 1

Call the unknown larger number l and the unknown smaller number s. From the problem statement, l + s = 30 and l/s = s. From the second of these equations, after multiplying both sides by s, l = s2. substituting this value into the first equation yields s2 + s = 30, or s2 + s - 30 = 0. Factoring shows the latter expression to be equivalent to (s + 6)(s - 5) = 0, which is true when s = -6 or s = +5. The latter value of s leads to l = 25, which satisfies the conditions of the problem without negative numbers. The former value of s leads to l = 36, which also satisfies the conditions of the problem.