SOLUTION: The sum of two numbers is 76. The second is 8 more than 3 times the first. What are the two numbers?

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Question 122885: The sum of two numbers is 76. The second is 8 more than 3 times the first. What are the two numbers?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If "The sum of two numbers is 76", then the first equation is x%2By=76

Also, if "The second is 8 more than 3 times the first", then the second equation is y=3x%2B8


So we have the system:



x%2By=76
y=3x%2B8



x%2B3x%2B8=76 Plug in y=3x%2B8 into the first equation. In other words, replace each y with 3x%2B8. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.


x%2B3x%2B8=76 Distribute


4x%2B8=76 Combine like terms on the left side


4x=76-8Subtract 8 from both sides


4x=68 Combine like terms on the right side


x=%2868%29%2F%284%29 Divide both sides by 4 to isolate x



x=17 Divide




Now that we know that x=17, we can plug this into y=3x%2B8 to find y



y=3%2817%29%2B8 Substitute 17 for each x


y=59 Simplify


So our answer is x=17 and y=59 which also looks like



Notice if we graph the two equations, we can see that their intersection is at . So this verifies our answer.


+graph%28+500%2C+500%2C+-5%2C+20%2C+-5%2C+62%2C+76-x%2C+3x%2B8%29+ Graph of x%2By=76 (red) and y=3x%2B8 (green)