Question

Each week, Allen earns $70 for every shift he works at the diner and $12 for every dog-walking job. He uses the expression 70x + 12y to keep track of his earnings. Part A: Identify the coefficients and variables in the expression. Part B: How many terms are in the expression, what are they, and how do you know? Part C: Which term in the expression shows the total earned from the diner?

Answer 1

A. coefficients: 70, 12; variables: x, y.

B. 2 terms: 70x, 12y; separated by an addition symbol

C. 70x

Explanation:

We will answer the questions in the context of this problem. In other problems, the meaning of "coefficient", "variable", and "term" may be different.

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A. The coefficients are the numbers; the variables are the letters. Then the coefficients are 70 and 12; the variables are x and y.

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B. Each product is a term. Terms are separated by the + sign. There are two terms in this expression, one on either side of the + sign. When an expression is written with no parentheses, the terms are separated by + or - signs. (Often, we think of the minus sign as being part of the coefficient of the term. Then we can say terms are separated by + signs. 10x + (-32y), for example.)

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C. When you match the coefficients to the numbers in the problem statement, you see that the number matching the earnings at the diner is $70 per shift. If we assume that x represents the number of shifts worked at the diner, then the term 70x will represent the total earned from the diner. It is the product of the earnings per shift and the number of shifts.