SOLUTION: One positive number is 6 more than twice another. If their product is 308, find the numbers. Small number? Large number?

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Question 927537: One positive number is 6 more than twice another. If their product is 308, find the numbers.
Small number?
Large number?
Answer by Techpriest(29) About Me  (Show Source):
You can put this solution on YOUR website!
In order to find the small number and large number, we must express it as an algebraic expression.
One positive number is 6 more than twice another of a number can be expressed as:
+y+=+6+%2B+2x+
If their product is 308:
+x%2Ay+=+308+
Through the expression shown above we can substitute y from the first equation to the second equation.
+x%286+%2B+2x%29+=+308+
+6x+%2B+2x%5E2%29+=+308+ Distributive Property of Multiplication
+2x%5E2+%2B+6x+=+308+ Reorder terms in order.
+%282x%5E2+%2B+6x%29%2F2+=+308%2F2+ Division Property of Equality
+x%5E2+%2B+3x+=+154+ Simplify
+x%5E2+%2B+3x+-+154+=+154+-+154+ Subtraction Property of Equality
+%28x%2B14%29%28x-11%29+ Factor
+x+=+-14%2C+x+=+11+ Zero Property
So, x = 11 or -14.
In order to find y, we substitute the x-value in the first equation for ALL solutions.
+y+=+6+%2B+2x+
+y+=+6+%2B+2%2811%29+
+y+=+6+%2B+22+
+y+=+28+
AND
+y+=+6+%2B+2%28-14%29+
+y+=+6+-+28+
+y+=+-22+
So, y = 28 or -22.
So, a solution of {11,28} or {-14,-22} can be plotted on a graph.
HOWEVER, the problem tells you that y is a positive number.
Since {11, 28} is positive. The small number assuming that it is x will be 11 and the large number assuming that it is y will be 28.