1720.41 – Patterned Equations

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

12×42=21×2413×62=31×26\begin{aligned}12 \times 42 &= 21 \times 24 \\13 \times 62 &= 31 \times 26\end{aligned}

Solution

Observe that in the equation 12×42=21×2412 \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 1414, something like:

14×xy=41×yx14 \times xy = 41 \times yx

Notice that in the given equations, the second number increased 2020 from 4242 to 6262. Let's try that. We find that 14×82=114814 \times 82 = 1148 and 41×28=114841 \times 28 = 1148. Voila! Thus,

14×82=41×2814 \times 82 = 41 \times 28

fits the pattern we found.

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