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?
If x = y+3+4.5x and y = x+18, what is the value of x/y?
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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.
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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Simplifying the first equation, we have: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
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
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