Question 1204546
Studio {{{A}}}

{{{classes}}}|{{{cost}}}
{{{3}}}|{{{ 70}}} 
{{{7}}}|{{{ 130 }}}
{{{8}}}|{{{ 145}}} 
{{{12}}}|{{{ 205}}}

equation:

{{{y=mx+b}}}

slope {{{m=(130-70)/(7-3)=15}}}

Studio {{{A}}} charges a mat fee of ${{{25}}}, so {{{b=25}}}

{{{y=15x+25}}}....eq.1


 Studio {{{B}}}

 {{{Classes}}}|{{{cost}}}
{{{4}}}|{{{ 80}}}
{{{6}}}|{{{ 120}}}
{{{9}}}|{{{ 180}}}
{{{ 11}}}|{{{ 220}}}

{{{y=mx+b}}}

slope {{{m=(120-80)/(6-4)=20}}}
 Studio {{{B}}} has no initial fee, so {{{b=0}}}

{{{y=20x}}}....eq.2
 

a system of equations

{{{y=15x+25}}}....eq.1
{{{y=20x}}}....eq.2
---------------------------left sides are equal, so
{{{15x+25=20x}}}
{{{25=20x-15x}}}
{{{5x=25}}}
{{{x=5}}}

 the two studios cost the same if the number of classes is <font color=red>5</font>

check

Studio {{{A}}}

{{{y=15*5+25=75+25=100}}}....eq.1

{{{Classes}}}|{{{cost}}}

 <font color=red>5</font>|<font color=red>100</font>


Studio {{{B}}}

{{{y=20*5=100}}}....eq.2

{{{Classes}}}|{{{cost}}}
 <font color=red>5</font>| <font color=red>100</font>