Question 1132495
3.	Anne and Stella both worked hard over the summer. Together, they earned a total of ${{{345}}}. Anne earned ${{{35}}} more than Stella. How much did each of them earn?

let’s  {{{x}}} be the amount Anne  earned and {{{y}}} be the amount Stella  earned 

(a)	Write a system of two equations with two variables to model this problem.

Together, they earned a total of ${{{345}}}=>

{{{x+y=345}}}....eq.1

Anne earned ${{{35}}} more than Stella

{{{x=y+35}}}......eq.2


(b)	Use substitution or the elimination method to solve the system.

substitute {{{x}}} from eq.2 in eq.1

{{{y+35+y=345}}}....eq.1.....solve for {{{y}}}

{{{2y+35=345}}}

{{{2y=345-35}}}

{{{2y=310}}}

{{{y=310/2}}}

{{{y=155}}}

now use eq.2 to find {{{x}}}

{{{x=y+35}}}......eq.2...substitute {{{155}}} for {{{y}}}

{{{x=155+35}}}

{{{x=190}}}


(c)	Graph both equations.

{{{drawing( 600, 600, -200, 400, -200, 400,
circle(190,155,.5),locate(190,155,p(190,155)),
 graph( 600, 600, -200, 400, -200, 400, x-35, -x+345) )}}}


(d)	Answer the question.

Anne earned ${{{190}}} and Stella earned ${{{155}}}