Question

One positive integer is 8 more than twice another. If their product is 384, find the numbers.

Answer 1

Answer: The numbers are 32 and 12

Explanation:

Let say those two positve integers are x and y.

x has to be 8 more than twice y , and that could be represent by the equation

x = 2y + 8

Their product is 384 meaning that x times y has to equal to 384 , and that can also be represented by the equation xy = 384

x = 2y + 8

xy = 384

Now using both equations, substitute the value for x into the second equation and solve for y.

(2y + 8)(y ) = 384

2y^2 + 8y = 384 Subtract 348 from both sides

-384 -384

2y^2 + 8y - 384 = 0 Factor the left sides by the GCF

2(y^2 + 4y - 192) = 0

x = -b ±
`√(b^2 -4ac ) /2`

The variables a= 1 , b=4 and c is -192

x = -4 ±
`√(784) /2`

x = -4 + 14 or x = -4 - 14

x = 12 or x = -16

Since we are dealing with length the value of y has to be 12.

Now that we know that y is 12 input 12 into one of the equations and solve for x.

x = 2(12) + 8

x = 24 + 8

x = 32