Which algebraic symbol best represents the word "product" when translating a verbal phrase into an algebraic expression?

Which phrase from the following sentence signals that you should introduce a variable to represent an unknown quantity? Sentence: "The number of apples a student picks."

Three times a number is 81. Use this phrase to write an equation and also solve for the unknown variable.

Translate and solve: "One third of a number plus four equals ten."

Translate the sentence and solve the resulting quadratic: "The product of a number and the difference of seven and that number is ten."