Question 934977
{{{a}}}= fraction of the job A can do in 1 day.
{{{b}}}= fraction of the job B can do in 1 day.
{{{c}}}= fraction of the job C can do in 1 day.
 
"A and B together can do a piece of work in 12 days" translates as
{{{12(a+b)=1}}}<--->{{{12a+12b=1}}}<--->{{{a+b=1/12}}} .
Since that is a job "which B and C together can do in 16 days" ,
{{{16(b+c)=1}}}<--->{{{16b+16c=1}}}<--->{{{b+c=1/16}}} .
"After A has been working at it for 5 days and B for 7 days, C finishes in 13 days" translates as
{{{5a+7b+13c=1}}} .
You get the system
{{{system(a+b=1/12,b+c=1/16,5a+7b+13c=1)}}} <---> {{{system(-5a-5b=-5/12,-2b-2c=-1/8,5a+7b+13c=1)}}} .
If you add all 3 equations, you get
{{{13c-2c=1-5/12-1/8}}}--->{{{11c=24/24-10/24-3/24}}}--->{{{11c=11/24}}}--->{{{c=1/24}}} .
Since C can do {{{1/24}}} of the joy each day,
C alone will do the work in {{{highlight(24 days)}}} .