System of Linear Equations

System of Linear Equations: Level 2 Challenges


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.

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

Shown right is a "magic square" in which the sums of each diagonal, each row, and each column are all equal.

Find \(y+z.\)

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

Bob weighs 100 pounds plus \(\frac{1}{2}\) of Sue's weight.

Sue weighs 100 pounds plus \(\frac{1}{3}\) of Bob's weight.

How much is their combined weight (in pounds)?

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