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Two positive numbers have a difference of 8 and a product of 33. What are these numbers?

A4 and 12
B3 and 12
C4 and 11
D3 and 11

Verified Answer :

hbrimley

knowing that 33 can only be the product of 1 and 33 or 11 and 3, the answer is 11 and 3 since 11-3 = 8 
but from an algebraic stand point here is how you solve it 
make x be one number and y be the other. You know 
x-y = 8 and 
x y = 33 
solve either equation for x or y, I will choose the first one and solve for x 
x - y = 8 
x = y+8 
now substitute that value of x in the second equation 
x y = 33 
(y+8) * y = 33 
y^2 + 8y = 33 
make the equation equal to 0 
y^2 + 8y - 33 = 0 
now factor the equation 
(y+11) (y-3) = 0 
your 2 solutions are 3 and -11, since the question says there are positive numbers, the solution for y is 3 
plug the y value (3) into either equation above and solve for x 
x - 3 = 8 
x = 11

school2019

It the answer is d 11-3=8
                            11*3=33