SOLUTION: Tyler said, "the sum of two numbers is 180 and twice the first number increased by forty is equal to to twice the second number." Help Tyler find the numbers.

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Tyler said, "the sum of two numbers is 180 and twice the first number increased by forty is equal to to twice the second number." Help Tyler find the numbers.       Log On


   

Question 170175: Tyler said, "the sum of two numbers is 180 and twice the first number increased by forty is equal to to twice the second number." Help Tyler find the numbers.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"the sum of two numbers is 180" translates to x%2By=180


"twice the first number increased by forty is equal to to twice the second number" translates to 2x%2B40=2y


2x%2B40=2y Start with the second equation


%282x%2B40%29%2F2=y Divide both sides by 2 to isolate y


%282x%29%2F2%2B%2840%29%2F2=y Break up the fraction.


x%2B20=y Reduce


So after isolating y, we get y=x%2B20


x%2By=180 Go back to the first equation


x%2Bx%2B20=180 Plug in y=x%2B20


2x%2B20=180 Combine like terms on the left side.


2x=180-20 Subtract 20 from both sides.


2x=160 Combine like terms on the right side.


x=%28160%29%2F%282%29 Divide both sides by 2 to isolate x.


x=80 Reduce. So this is the first answer.


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y=x%2B20 Go back to the isolated equation


y=80%2B20 Plug in x=80


y=100 Add. This is the second answer.


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Answer:

So the solutions are x=80 and y=100 which means that the two numbers are 80 and 100