SOLUTION: Twice the larger number is 3 more than five times the smaller number. The sum of the 2 numbers is 4 times the larger number. What are the two numbers?

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Question 161181: Twice the larger number is 3 more than five times the smaller number. The sum of the 2 numbers is 4 times the larger number. What are the two numbers?
Answer by schrammbledeggs(41) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = larger number
Let y = smaller number
2x = 3 + 5y (first sentence transformed into an equation)
x + y = 4x (second sentence transformed into an equation)
Let's solve for y first by rearranging the 2nd equation into:
x + y - x = 4x - x
y = 3x
Substitute that value of y into the first equation:
2x = 3 + 5(3x)
2x = 3 + 15x
2x - 15x = 3 + 15x - 15x
-13x = 3
x = -3/13
Plug that back into the 2nd equation we got earlier...
y = 3x
y = 3(-3/13)
y = -9/13
So the larger number = -3/13 and the smaller number = -9/13