SOLUTION: One number is 12 more than a another. the sum of the smallest number and twice the larger number is 39. find the larger number x + 12 = y x + 2(y)= 39 Am I on the right tra

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: One number is 12 more than a another. the sum of the smallest number and twice the larger number is 39. find the larger number x + 12 = y x + 2(y)= 39 Am I on the right tra      Log On


   

Question 109230: One number is 12 more than a another. the sum of the smallest number and twice the larger number is 39. find the larger number
x + 12 = y
x + 2(y)= 39
Am I on the right track for solving this problem?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You set it up perfectly

Start with the given system
x%2B2y=39
y=x%2B12



x%2B2%28x%2B12%29=39 Plug in y=x%2B12 into the first equation. In other words, replace each y with x%2B12. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


x%2B2x%2B24=39 Distribute


3x%2B24=39 Combine like terms on the left side


3x=39-24Subtract 24 from both sides


3x=15 Combine like terms on the right side


x=%2815%29%2F%283%29 Divide both sides by 3 to isolate x



x=5 Divide




Now that we know that x=5, we can plug this into y=x%2B12 to find y



y=%285%29%2B12 Substitute 5 for each x


y=17 Simplify


So our answer is x=5 and y=17


So our two numbers are 5 and 17