Find two positive numbers so that twice their sum equals their product and one number is 3 times the other number. Enter the sma
2 answers:
Answer: 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
<u>The positive numbers are 8/3 and 8</u>.
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