\(\mathrm{Write\:the\:equation:}\)
\(0.5x+x+3x=180\)
\(\mathrm{Add\:similar\:variable:}\)
\(4.5x=180\)
\(\mathrm{Multiply\:both\:sides\:by\:}10:\)
\(4.5x\cdot \:10=180\cdot \:10\)
\(\mathrm{Simplify:}\)
\(45x=1800\)
\(\mathrm{Divide\:both\:sides\:by\:}45:\)
\(\frac{45x}{45}=\frac{1800}{45}\)
\(\mathrm{Simplify}:\)
\(x=40\)
\(\mathrm{Rewrite\:the\:equation\:with\:}y\)\(:\)
\(3\cdot 40+0.5\cdot 40+40+3\cdot \:40+40+0.5y=360\)
\(\mathrm{Multiply\:the\:numbers:}\)
\(240+20+40+40+0.5y=360\)
\(\mathrm{Add\:the\:numbers:}\)
\(0.5y+340=360\)
\(\mathrm{Multiply\:both\:sides\:by\:to\:make\:0.5\:a\:whole\:number\:}10:\)
\(0.5y\cdot \:10+340\cdot \:10=360\cdot \:10\)
\(\mathrm{Simplify\:}:\)
\(5y+3400=3600\)
\(\mathrm{Subtract\:}3400\mathrm{\:from\:both\:sides}: \)
\(5y+3400-3400=3600-3400\)
\(\mathrm{Simplify}\)\(\;:\)
\(5y=200\)
\(\mathrm{Divide\:both\:sides\:by\:}5\) \(:\)
\(\frac{5y}{5}=\frac{200}{5}\)
\(\mathrm{Simplify}\) \(:\)
\(y=40\)
.
