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Two positive numbers have a difference of 8 and a product of 48 Find the two numbers?
This problem can be solved with a system of equations. Let the first number equal x and the second number equal y. Here are the two equations:
x-y=8 This makes sense because if two number have a difference of 8, than the first number minus the second number will equal 8.
x * Y = 48 This is self explanatory.
Now, we solve:
x-y=8
x=8+y (y is added to both sides. Now we know what x is equal to, so we can substitute it into the second equation)
(8+y)*y=48
8y+y2=48 (y is distributed)
y2+8y-48=0 (the equation is made into a quadratic)
(y+12)(y-4)=0 (the equation is factored)
We know y is equal to four and not -12 because both number are positive.
Now we solve for x:
x-4=8
x=12
Therefore, your two number are 12 and 4.
What else can I help you with?
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