SOLUTION: There are two numbers whose sum is 50. Three times the first is five more than twice the second. What are the numbers? Please DO answer quickly.

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Question 165268: There are two numbers whose sum is 50. Three times the first is five more than twice the second. What are the numbers?
Please DO answer quickly.
Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"There are two numbers whose sum is 50" ---> x%2By=50

"Three times the first is five more than twice the second" ---> 3x=2y%2B5


x%2By=50 Start with the first equation.


y=50-x Subtract x from both sides.


3x=2y%2B5 Move onto the second equation


3x=2%2850-x%29%2B5 Plug in y=50-x


3x=100-2x%2B5 Distribute.


3x=-2x%2B105 Combine like terms on the right side.


3x%2B2x=105 Add 2x to both sides.


5x=105 Combine like terms on the left side.


x=%28105%29%2F%285%29 Divide both sides by 5 to isolate x.


x=21 Reduce.


y=50-x Go back to the previously isolated equation


y=50-21 Plug in x=21


y=29 Subtract


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Answer:

So the solutions are x=21 and y=29 which form the ordered pair (21,29)

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
call the numbers a and b. a+b=50 so a=50-b (3 times a)(3a)=5+(2 times b)(2b)
re written as 3a=5+2b. Now substituting a's value from first equation into 2nd equation we get 3(50-b)= 5+2b or 150-3b=5+2b adding 3b and subtracting 5 from each side we get 5b=145 so b =29 so since a=50-b(29) the a =21
answer: a=21 and b=29