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System of Linear Equations

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?

Level 2

         

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

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

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

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

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

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?

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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