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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?

System of Linear Equations: Level 2 Challenges

         

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?

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

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

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

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

A full bottle of green tea weighs 350 grams.
With half the tea consumed, it weighs 200 grams.

What is the weight of the empty bottle?

In splitting up $1000, a group of three married couples agrees upon the following plan:

The wives receive a total of $396, of which Mary gets $10 more than Diane, and Ellen gets $10 more than Mary.

Bill Brown gets twice as much as his wife, Henry Hobson gets the same as his wife, and John Jones gets 50 percent more than his wife.

What are the full names of the three wives?

Note: Assume that the wives have the same last names as their husbands.

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