Question 170175
"the sum of two numbers is 180" translates to {{{x+y=180}}}



"twice the first number increased by forty is equal to to twice the second number" translates to {{{2x+40=2y}}}



{{{2x+40=2y}}} Start with the second equation



{{{(2x+40)/2=y}}} Divide both sides by 2 to isolate y



{{{(2x)/2+(40)/2=y}}} Break up the fraction.



{{{x+20=y}}} Reduce



So after isolating y, we get {{{y=x+20}}}



{{{x+y=180}}} Go back to the first equation



{{{x+x+20=180}}} Plug in {{{y=x+20}}}



{{{2x+20=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=(160)/(2)}}} Divide both sides by {{{2}}} to isolate {{{x}}}.



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



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{{{y=x+20}}} Go back to the isolated equation



{{{y=80+20}}} 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