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# SAT Prep

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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