SOLUTION: The difference of two problems is 33. The second is 7 less than 3 times the first. What are the two numbers?

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Question 112245: The difference of two problems is 33. The second is 7 less 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!
Translate the following:

"The difference of two problems is 33"---> y-x=33
"The second is 7 less than 3 times the first"---->y=3x-7




Start with the given system
y-x=33
y=3x-7



%283x-7%29-x=33 Plug in y=3x-7 into the first equation. In other words, replace each y with 3x-7. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2x-7=33 Combine like terms on the left side


2x=33%2B7Add 7 to both sides


2x=40 Combine like terms on the right side


x=%2840%29%2F%282%29 Divide both sides by 2 to isolate x



x=20 Divide




Now that we know that x=20, we can plug this into y=3x-7 to find y



y=3%2820%29-7 Substitute 20 for each x


y=53 Simplify


So our answer is x=20 and y=53


So the two numbers are 20 and 53