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Problem 36

$$
\begin{aligned} \text { Find the ratio of } x \text { to } y : \frac{4}{y}+\frac{3}{x} &=44 \\ & \frac{12}{y}-\frac{2}{x}=44 \end{aligned}
$$

Answer

$\frac{x}{y}=\frac{5}{8}$


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Video Transcript

Okay, so in this problem, it wants us to find the issue of extra. Why, if score score over Why? Plus three over X equals 44 and 12 over. Why? Minus two over X. Egan's 44. Okay, there are a lot of ways to do this problem. Um, some people may up to get a common denominator and solved that way what I was thinking of actually doing here rate waas, um, subtracting the two equations from each other. Okay. And getting negative eight over. Why? Plus five over acts equal zero. Remember, when I subtract here, I'm changing or my sign. So be really, really careful with your signs here. Okay? So I'm gonna bring this over to the next page. Okay? Negative. Eat over. Why? I plus five over X equals zero negative e eight over. Why? Plus five over X equals zero. I'm gonna bring this to the other side. Just don't, So it's not negative. So I get five over X equals e over. Why? Remember, this was negative. Now it becomes positive when it moves to the other side. And when I cross multiply, I get five. Y equals. He acts and it wants the ratio of extra Why? So if I divide by why here and I divide by eight here I get the ratio of xto. I is five t again a very algebraic way of doing.