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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

         

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.

\[ \begin{array} { c c c c c c c } 3a &+& 7b &+ &c &= & 315 \\ 4a &+& 10b &+& c &= & 420 \\ a &+& b &+& c &= & ? \end{array} \]

I have a secret set of 3 integers. If I add every possible pairing of them, I get the numbers \[ 0,\ 4,\ 10. \] What is the absolute difference between the largest two of my secret numbers?

\[\large \begin{align} \color{blue}{x} + 2\color{green}{y} + 4\color{red}{z} &= 7 \\ 3\color{blue}{x} + 5\color{green}{y} + 7\color{red}{z} &= 9 \\ 9\color{blue}{x} + 6\color{green}{y} + 2\color{red}{z} &= 10 \\ \color{blue}{x}+\color{green}{y}+\color{red}{z} &= \ ? \end{align}\]

If \(3m+2n+4s=26\) and \(6n+4m+2s=48\), then what is \(m+n+s\)?

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