1720.41 – Patterned Equations

Find the pattern in these two equations and then make up one more of your own.

\begin{aligned} 12 \times 42 &=& 21 \times 24, \\ 13 \times 62 &=& 31 \times 26. \end{aligned}

Solution

Observe that in the equation $12 \times 42 = 21 \times 24$ the numbers on one side are the reverse of the numbers on the other side. The same is true of the second given equation.

The next one ought to involve $14$ , something like:

$14 \times xy = 41 \times yx.$

Notice that in the given equations, the second number increased $20$ from $42$ to $62$ . Let's try that. We find that $14 \times 82 = 1148$ and $41 \times 28 = 1148$ . Voila! Thus,

$14 \times 82 = 41 \times 28.$

fits the pattern we found.

You can keep going and you might find a formula for all of these.