I pick two whole numbers x and y between 1 and 10 inclusive (not necessarily distinct). My friend picks two numbers x -4 and 2y-1. If the product of my friend's numbers is one greater than the product of my numbers, then what is the product of my numbers?
+23246 The product of your two numbers, x and y, must be one more than the product of your friend's numbers, (x - 4) and (2y - 1).
Putting this into an equation: xy = (x - 4)(2y - 1) + 1
Multiplying out: xy = 2xy - x - 8y + 4 + 1
Simplifying: xy = 2xy - x - 8y + 5
Subtracting xy: 0 = xy - x - 8y + 5
Adding x: x = xy - 8y + 5
Subtracting 5: x - 5 = xy - 8y
Factoring: x - 5 = y(x - 8)
Dividing by x - 8: (x - 5) / (x - 8) = y
Using the formula: y = (x - 5) / (x - 8).
Replace x with the possibilities: 1, 2, 3, ..., 10
You will find that 9 will be a possiblity for x; this will give you the value for y.
THX SO MUCH GENO3141!!!!!!!!!!!!! YOU ARE THE ONLY PERSON (unless cphill) THAT HELPED ME THE MOST!!!!! I APRECIATE IT!
+23246 The product of your two numbers, x and y, must be one more than the product of your friend's numbers, (x - 4) and (2y - 1).
Putting this into an equation: xy = (x - 4)(2y - 1) + 1
Multiplying out: xy = 2xy - x - 8y + 4 + 1
Simplifying: xy = 2xy - x - 8y + 5
Subtracting xy: 0 = xy - x - 8y + 5
Adding x: x = xy - 8y + 5
Subtracting 5: x - 5 = xy - 8y
Factoring: x - 5 = y(x - 8)
Dividing by x - 8: (x - 5) / (x - 8) = y
Using the formula: y = (x - 5) / (x - 8).
Replace x with the possibilities: 1, 2, 3, ..., 10
You will find that 9 will be a possiblity for x; this will give you the value for y.
