+0  
 
0
34
2
avatar

The sum of two numbers is 235, and the difference of the same two numbers is 41. Find these numbers.

 Nov 7, 2021
 #1
avatar
+1

a+b = 235

a-b =41           Add the equations together then solve for 'a'      then use this answer to solve for 'b'

 Nov 7, 2021
 #2
avatar+390 
+2

Hello Guest,

 

The sum of two numbers is 235, and the difference of the same two numbers is 41. Find these numbers.

 

\(a+b=235\)

\(a-b=41\)

 

\(\mbox {You can change the variables by the first equation.}\)

 

\(b+a=235\)

\(a-b=41\)

 

\(b+a=235\)

\(-b+a=41\)

 

\(\mbox {Subtract a from the first equation.}\)

 

\(b=-a+235\)

\(-b+a=41\)

 

\(\mbox {Substitute } b=-a+235 \mbox { in the second equation.}\)

 

\(b=-a+235\)

\(2a-235=41\)

 

\(\mbox {Add } 235 \mbox { by } 41\)

 

\(b=-a+235\)

\(2a=276\)

 

\(\mbox {Solve for a}\)

 

\(b=-a+235\)

\(a=138\)

 

\(\mbox {Substitute } a \mbox { into the first equation. }\)

 

\(b=97\)

\(a=138\)

 

\(\mbox {This equation was solved with the variables a and b having the values } (a,b)=(138,97) \mbox { . }\)

 

Straight

 Nov 9, 2021

9 Online Users

avatar