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In the figure, what is the value of y?

 

 Mar 27, 2021
 #1
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3x + 0.5x + x = 180

x = 40

0.5x = 0.5y = 20

y = 40º

 Mar 28, 2021
 #2
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\(\mathrm{Write\:the\:equation:}\)

\(0.5x+x+3x=180\)

\(\mathrm{Add\:similar\:variable:}\)

\(4.5x=180\)

\(\mathrm{Multiply\:both\:sides\:by\:}10:\)

\(4.5x\cdot \:10=180\cdot \:10\)

\(\mathrm{Simplify:}\)

\(45x=1800\)

\(\mathrm{Divide\:both\:sides\:by\:}45:\)

\(\frac{45x}{45}=\frac{1800}{45}\)

\(\mathrm{Simplify}:\)

\(x=40\)

\(\mathrm{Rewrite\:the\:equation\:with\:}y\)\(:\)

\(3\cdot 40+0.5\cdot 40+40+3\cdot \:40+40+0.5y=360\)

\(\mathrm{Multiply\:the\:numbers:}\)

\(240+20+40+40+0.5y=360\)

\(\mathrm{Add\:the\:numbers:}\)

\(0.5y+340=360\)

\(\mathrm{Multiply\:both\:sides\:by\:to\:make\:0.5\:a\:whole\:number\:}10:\)

\(0.5y\cdot \:10+340\cdot \:10=360\cdot \:10\)

\(\mathrm{Simplify\:}:\)

\(5y+3400=3600\)

\(\mathrm{Subtract\:}3400\mathrm{\:from\:both\:sides}: \)

\(5y+3400-3400=3600-3400\)

\(\mathrm{Simplify}\)\(\;:\)

\(5y=200\)

\(\mathrm{Divide\:both\:sides\:by\:}5\) \(:\)

\(\frac{5y}{5}=\frac{200}{5}\)

\(\mathrm{Simplify}\) \(:\)

\(y=40\)

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 Apr 4, 2021

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