Find two positive numbers so that twice their sum equals their product and one number is 3 times the other number. enter the smaller number first.

8/3 and 8

Step-by-step explanation: Suppose that the two numbers are represented by P and Q.

Twice their sum equals their product: 2(P + Q) = PQ

One number is 3 times the other: P = 3Q

To solve it, first, substitute P in the first equation:

2(P+Q) = PQ

2(3Q + Q) = 3Q.Q

2(4Q) = 3Q²

8Q = 3Q²

3Q² - 8Q = 0

Q(3Q - 8) = 0

Q = 0

3Q - 8 = 0

Q = 8/3

As the question said the numbers are positive and since 0 isn't positive or negative, to find P, use Q=8/3

P = 3Q

P = 3.

P = 8

The positive numbers are 8/3 and 8.