Question

The average of an electrician's hourly wage and a plumber's hourly wage is $24. One day a contractor hires an electrician for 7 hr of work and the plumber for 5 hr of work and pays a total of $266 in wages. Find the hourly wage for the electrician and for the plumber.

Answer 1

$\blacksquare\,\,\,\,\,\,\,\,\,Let\,\,the\,\, hourly\,\,wage\,\,of\,\,an\,\, electrician\,\,is,\\\$ \,x\,\,and \,\,the\,\, hourly\,\,wage\,\,of\,\,a\,\,plumber\,\,is,\,\,\$\,y\,\,.\\\\ According\,\, to\,\,the\,\, question,\,\, average\,\, hourly\,\,wage\\of\,\,the \,\, electrician\,\,and\,\,the\,\,plumber\,\,is,\,\,\$\,24\,.\\\\\therefore \,\,\frac{x+y}{2}\,=\,24\\\\\Rightarrow\,x+y\,=\,48\\\\\Rightarrow \,y\,=\,48-x\hspace{10pt}\cdot\cdot\cdot\cdot\cdot\cdot\cdot\cdot(i)\\\\One day\,\,a\,\,contructor\,\,hires\,\,an\,\, electrician\,\,for\\7\,\,hrs. \,\,and\,\,a\,\,plumber\,\,for\,\,5\,\,hrs.\,\,and\,\,pays\,\,total\\\$\,266\,.\\\\ \therefore\,\,7x+5y\,=\,266\hspace{10pt}\cdot\cdot\cdot\cdot\cdot\cdot\cdot\cdot\cdot(ii)\\\\ Now,\,\,from\,\,(i)\,\,and\,\,(ii)\,\,we\,\,have,\\\\7x+5(48-x)\,=\,266 \\\\\Rightarrow\,7x+240-5x\,=\,266\\\\\Rightarrow\,2x\,=\, 266-240\\\\\Rightarrow\,2x=\,26\\\\\Rightarrow\,x\,=\, \frac{26}{2}\\\\\Rightarrow\,x\,=13\\\\Now,\,\,put\,\,x=13\,\,in\,\,(i)\,\,then,$

Y = 48 – 13 → y = 35 :. The hourly wage of the electrician is, $ 13 and the hourly of the plumber is, $35.

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