SOLUTION: If one number is equal to two times a second number. Two times the first number plus two times the second number is 24. If you let x stand for the first number and y for the second

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Question 175696: If one number is equal to two times a second number. Two times the first number plus two times the second number is 24. If you let x stand for the first number and y for the second, what are the two numbers?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"one number is equal to two times a second number" translates to x=2y


"Two times the first number plus two times the second number is 24" means that 2x%2B2y=24



So we have the system:

x=2y
2x%2B2y=24




2%282y%29%2B2y=24 Plug in x=2y into the second equation. In other words, replace each x with 2y. Notice we've eliminated the x variables. So we now have a simple equation with one unknown.


4y%2B2y=24 Distribute


6y=24 Combine like terms on the left side


y=%2824%29%2F%286%29 Divide both sides by 6 to isolate y


y=4 Divide


Now that we know that y=4, we can plug this into x=2y to find x



x=2%284%29 Substitute 4 for each y


x=8 Multiply


So our answer is x=8 and y=4 which means that the first number is 8 and the second number is 4.