The secret behind Emily’s puzzle is the order of operations, a fundamental mathematical principle that determines how calculations should be performed. Many people remember this rule through the abbreviations PEMDAS or BODMAS, which refer to parentheses, exponents, multiplication, division, addition, and subtraction. Although the abbreviations may differ, the underlying rules remain the same. Multiplication and division have equal priority and are performed from left to right, while addition and subtraction are completed afterward.

Let’s examine Emily’s expression carefully. It contains subtraction, division, and multiplication, but no parentheses or exponents. Therefore, we must deal with division and multiplication before subtraction. Starting from the left, the first operation to complete is 40 divided by 10. That calculation gives us four, meaning the expression can now be rewritten in a much simpler form:

At this point, another common mistake can occur. Someone might subtract four from 80 immediately, but that would ignore the priority of multiplication. Instead, we multiply four by four, giving us 16. Only then can we complete the subtraction. Our final calculation becomes 80 minus 16, which equals 64. The puzzle is not testing complicated mathematical knowledge. Rather, it demonstrates how following a few basic rules makes even potentially confusing calculations straightforward.

The correct answer is that Emily is 64 years old.

Someone who calculates every operation strictly from left to right would arrive at 16, but that method does not follow standard mathematical conventions. Puzzles like this are entertaining because they remind us how easily familiar information can be overlooked when we rush. They also encourage concentration, patience, and logical thinking.

The lesson is simple: solving a problem quickly isn’t always the same as solving it correctly. Sometimes, slowing down and remembering the basics makes all the difference.