Then your teacher said, “Let x be the number of goats….”
He started writing stuff on the board with numbers and plus signs and x‘s, and you just kept thinking, “x is a letter, not a number.”
In graduate school, I had the opposite experience. I was in a course on special functions, such as the zeta function. I was busily taking notes when my professor, the dear Dr. Kupershmidt, wrote an unfamiliar symbol on the board. I puzzled for a moment, and then I asked, “What is that symbol?” He said, “That’s a six.”
As in the number six. I hadn’t seen one of those in a while. Most of what was on the board was letters (of the Greek variety) and mathematical operation symbols. As for numbers, there were 0s, 1s, and 2s, for sure, but a 6? It had been a while.
But, back to you and that x. Why not just use a number if we are going to talk about numbers? Well, we get tired of writing long phrases describing unknown quantities.
“Jakob had 27 goats, one more than twice as many goats as the number of goats Eric had.” seems like a lot to say compared to an equation.
The variable, x, is a container for the unknown. It is like the visa gift card you received from your uncle who forgot to mention how much was on it. You carry it around thinking of it just like money, an unknown amount, but money nonetheless.
Finding x is the name of the game.
With variables close, algebra is not far. Our word “algebra” comes from “al-jabr” meaning “completion,” used by 9th century Persian mathematician al-Khwarizmi. Check out Derbyshire’s Unknown Quantity for a history of the use of variables, equations, and algebra.