Question

The product of two numbers is 392. The quotient of the two numbers is 2. What are the two numbers?

Answer 1

Step-by-step explanation:

y=[a×b=392 and a/b=2]

ASSUMPTIONS

Let “a, b” be the two numbers

OBSERVATIONS/SUFFICIENT CONDITIONS

Solve this problem using a system of equations or by substitution

CALCULATIONS

y=[a×b=392 and a/b=2]

a=2b

2b×b=392

2b^2=392

2b^2/2=392/2

b^2=196

+/- √(b^2=196)

b=+/- 14

Now, if b=+/- 14, then a= 2b yields a=+/- 28

So, by substitution,

y@ a×b=392 yields

y=[+/- 28×+/- 14=392] and

a, b={+/- 28, +/- 14}

PROOF

If a, b={+/- 28, +/- 14}, then the equations

a/b=2

+/- 28/+/- 14=2 and

2=2 establish the roots (zeros) a, b={+/- 28, +/- 14} of the expressions y=[a×b=392 and a/b=2]

C.H.

Answer 2

Answer:

14 and 28

Step-by-step explanation:

let x and y be two numbers

x/y= 2______1           xy= 392________2

x= 2y

2x^2= 392

x^2= 196

x= 14 and y= 2x= 2(14)= 28