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If one Bitcoin and 100,000 Dogecoin are worth $480, and two Bitcoin and 150,000 Dogecoin are worth $948, would you rather have one Bitcoin or 100,000 Dogecoin?

\[ \begin{eqnarray} \frac{1}{x} + \frac{1}{y} &=& \frac{1}{3}\\ \frac{1}{x} + \frac{1}{z} &=& \frac{1}{5}\\ \frac{1}{y} + \frac{1}{z} &=& \frac{1}{7} \\ \end{eqnarray} \]

Given the system of equations above, what is the value of \( \frac{z}{y}\)?

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\[ \large{\begin{cases} x + y + u = 4 \\ y + u + v = -5 \\ u + v +x = 0 \\ v + x + y = -8 \end{cases}} \]

Let \(x,y,u\) and \(v\) be numbers satisfying the system of equations above. Find the product \(xyuv\).

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Above is a "magic square" in which the sum of each diagonal, each row, and each column are all equal. Find \(y+z.\)

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Today, in a 10-member committee, an old member was replaced by a young member. As such, the average age is the same today as it was 4 years ago.

What is the (positive) difference in ages between the new member and the replaced old member?

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At 6pm, 15 boys left school, and then the remaining children could be split evenly into groups each containing 2 girls and 1 boy.

At 7pm, 45 girls left school, and then the remaining children could be split evenly into groups each containing 1 girl and 5 boys.

How many boys were there *before* 6pm?

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