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Call the two numbers required m and n. Then from the problem statement, m = 25 - n (equation 1) and mn = 100 (equation 2). Substitute the expression for m in equation 1 into equation 2 to produce n(25 - n) = 100. Multiply out the left side to produce 25 n - n2 = 100. Multiply this equation by -1 and collect all terms on one side to produce n2 - 25n -100 = 0 (equation 3). Equation 3 factors into (n -20)(n-5) = 0, which is true when n = 20 or n = 5. From equation 1 again, this means m = 5 or 20 respectively. Therefore, the two numbers required are 5 and 20.

Check: 5 + 20 = 25; 5 X 20 = 100.

Q: What two number times each other equal 100 and added together equal 25?

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