The product of a number and the number 8More than it is 105
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Sharif O. asked • 06/16/16
One number is 8 greater than another. The product of the numbers is 105. Find the numbers.
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Kenneth S. answered • 06/16/16
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Surely you must have seen problems of this kind begin by saying LET x be one number; then another is x+8 (eight more than first number).
Now that's established, the product of these is 105. That means, in our algebraic system, x(x+8) = 105.
Using the wonderful distributive property (or law); x2+8x = 105.
We can put all terms on one side to get a quadratic equation (& then hope that we can factor it):
x2+8x-105=0
(x+15)(x-7) = 0.
Using the beloved Zero Product Property, we get two answers; x = 7 or x = -15.
We have two solutions, therefore: larger number is 15, smaller number is 7, OR
larger number is -7, smaller number is -15.
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