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If x = y+3+4.5x and y = x+18, what is the value of x/y?

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If x = y+3+4.5x and y = x+18, what is the value of x/y?

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If x = y+3+4.5x and y = x+18, what is the value of x/y?

A. -6/5
B. -7/20
C. 1/4
D. 5/6
E. 1.5

The OA is the option B.

Is there a strategic approach to solving this PS question? Could anyone give me some help here?

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Hello Vjesus12.

Let's take a look at your question.

We have to solve this two-equation system: $$x=y+3+4.5x\ \ \ --\ --\left(1\right)$$ $$y=x+18\ \ \ --\ --\left(2\right)$$ If we replace the second equation into the first one we get $$x=\left(x+18\right)+3+4.5x\ \ \ \Rightarrow\ \ \ \ x=21+5.5x$$ $$-21=5.5x-x\ \ \ \Rightarrow\ \ \ \ -21=4.5x\ \ \ \Rightarrow\ \ \ x=-\frac{21}{4.5}.$$ Now, we can find the value of y as follows: $$y=x+18\ \ \Rightarrow\ \ \ y=-\frac{21}{4.5}+18\ =\ \frac{60}{4.5}.$$ Finally, we can get the value of x/y $$\frac{x}{y}=\frac{-\frac{21}{4.5}}{\frac{60}{4.5}}=-\frac{21}{60}=-\frac{7}{20}.$$ This implies that the correct answer is the option B.

I hope it is clear enough.

Regards.

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VJesus12 wrote:
If x = y+3+4.5x and y = x+18, what is the value of x/y?

A. -6/5
B. -7/20
C. 1/4
D. 5/6
E. 1.5
Simplifying the first equation, we have:

x = y + 3 + 4.5x

-3.5x = y + 3

Substituting x + 18 for y, we have:

-3.5x = x + 18 + 3

-4.5x = 21

x = 21/-4.5 = -210/45 = -14/3

Thus, y = -14/3 + 18 = 40/3.

So x/y = (-14/3)/(40/3) = -14/40 = -7/20.

Answer: B

_________________
Scott Woodbury-Stewart Founder and CEO

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