The reason why Mathematics is required for so many subjects is that it can be used to solve problems outside of mathematics, the dreaded word problems . There will be many word problems in this class, usually leading to a mathematical problem of the kind we are discussing at the time. Students don't like word problems because they involve the extra layer of converting the word problem to a math problem. But keep in mind that math classes are the only kind of classes you take where some problems are not word problems!
This first word problem of this course can be solved by deriving and solving an equation, but it can also be solved essentially by guessing and modifying the answer until it fits, without any algebraic manipulation. We will revisit it in the future in a more complicated setting.

You buy a pot and its lid for a total of $ 11. The sales person tells you that the pot by itself costs $ 10 more than the lid. The price of the pot is $ and the price of the lid is $ .