Chapter 5: Systems of Equations

5.7 Solving Internet Game Puzzles

The internet has many of the following picture number puzzles. All are quickly and easily solved with the strategies used for solving systems of equations. What are the solutions for the following picture puzzles?

1. $\begin{array}{ccccccr} \text{horse}&+&\text{horse}&+&\text{horse}&=&30 \\ \text{horse}&+&\text{two horseshoes}&+&\text{two horseshoes}&=&18 \\ &&\text{two horseshoes}&-&\text{two boots}&=&2 \\ \text{boot}&+&\text{horse}&\times &\text{horseshoe}&=&? \end{array}$

2. $\begin{array}{ccccccr} \text{bottle}&+&\text{bottle}&+&\text{bottle}&=&30 \\ \text{bottle}&+&\text{hamburger}&+&\text{hamburger}&=&20 \\ \text{hamburger}&+&\text{two mugs}&+&\text{two mugs}&=&9 \\ \text{hamburger}&+&\text{mug}&\times&\text{bottle}&=&? \end{array}$
3. A more challenging system of equations is the four-by-four puzzle shown below. Each individual row and column are summed to the number in either row or column 5. Find the five missing numbers and place them in their correct positions.
Rows Column 1 Column 2 Column 3 Column 4 Column 5
Row 1 $a$ $2b$ $-c$ $d$ ?
Row 2 $2d$ $-a$ $-2b$ $-2c$ $-8$
Row 3 $c$ $-d$ $a$ $b$ ?
Row 4 $-b$ $-c$ $-d$ $2a$ $5$
Row 5 $-1$ ? $3$ ? ?