SOLUTION: a number is subtracted from 20 and from 17.the product of the numbers so obtained is 180.find the original number

Question 992141: a number is subtracted from 20 and from 17.the product of the numbers so obtained is 180.find the original number
Answer by ikleyn(52855) (Show Source): You can put this solution on YOUR website!
.
(20-x)*(17-x) = 180.

180 = 12*15 is an appropriate factorization of 180 into the product of two numbers that differs in 3.

So, 20-x = 15 (greater of these two factors),

which implies

x = 5.

180 = (-12)*(-15) is also an appropriate factorization of 180 into the product of two numbers that differs in 3.

So, 20-x = -12,

which implies

x = 32.

Answer. Two solutions are x=5 and x=32.

P.S. Surely, you can solve the quadratic equation above by using the quadratic formula.

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