Mrs. Jones gave this homework project to her college students:

Discover the sample behind these wrong-looking equations:
$$56+43+2+16=5+85+6+1+99$$
$$27+16+117=6+76+117$$
After which provide you with two wrong-looking equations of your individual that fulfill the identical sample.

Bobby was stumped, however he remembered that Mrs. Jones had been educating this course nearly the very same means for 30 years, and that she taught his dad too. He went residence, dug by his dad’s outdated papers, and copied his dad’s (appropriate) resolution to a really similar-looking project as his personal:

$$7+8+107=102+92+7+16$$
$$35+109+53=5+44+10+53$$

When Mrs. Jones first checked Bobby’s solutions, she simply thought they had been unsuitable. However after excited about what error he might have made, she realized what he had carried out.

What was the sample behind the equations, and what did Mrs. Jones understand about Bobby’s solutions?