Question 686427

 Lucy took three tests. If her median score was 82, her mean score was 87, and the range was 17, what were her three test scores? 

let   three tests be {{{a}}}, {{{b}}}, and {{{c}}}

the median (being the middle value, in your case {{{b}}})score was {{{82}}}:

{{{82=b}}}......................1


the mean (average) was {{{87}}}:

87=(a+b+c)/3...................2

and the range (  the difference between the two most extreme values)was {{{17}}}:

let’s {{{a>b>c}}}

so.   the range  is the difference between {{{a}}} and {{{c}}}


{{{17=a-c}}}.......................3
______________________________

solve the system:

{{{82=b}}}......................1.......plug it in 2

87=(a+b+c)/3...................2

{{{17=a-c}}}.......................3
_________________

87=(a+82+c)/3...................2a

take 3 and solve for {{{c}}}

{{{17=a-c}}}.......................3

{{{c=a-17}}}...................plug it in 3a



{{{87=(a+82+a-17)/3}}}...................2a.......solve for {{{a}}}

{{{87*3=2a+82-17}}}

{{{261=2a+65}}}

{{{261-65=2a}}}

{{{196/2=a}}}

{{{a=98}}}

now, go to 3a and find {{{c}}}


{{{c=a-17}}}

{{{c=98-17}}}

{{{c=81}}}


so, her three test scores {{{a=98}}},{{{b=82}}}, and {{{c=81}}}