A box containing 10 physics textbooks and 3 physics workbooks weighs 50.1 pounds. A box containing 8 physics textbooks and 12 physics workbooks weighs 51.9 pounds. The weight of each box when empty is 1.5 pounds. How much does each textbook and each workbook weigh? Complete the explanation for how you solved this problem.

Step-by-step explanation:

Subtracting the weight of the box from each of the totals, we can write the equations of weight of the different boxes as ...

  10x +3y = 48.6

  8x +12y = 50.4

where x and y are the weights of a textbook and workbook, respectively.

There are a variety of ways to solve these equations. One of my favorite is to use a graphing calculator (see attached). You can also do it using elimination or substitution. Let's try substitution.

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Solving the first equation for 3y, we get ...

  3y = 48.6 -10x

Recognizing that 12y = 4(3y), we can substitute this into the second equation:

  8x +4(48.6 -10x) = 50.4

  194.4 -32x = 50.4 . . . . . . . eliminate parentheses

  144 = 32x . . . . . . . . . . . . . . add 32x -50.4

  4.5 = x . . . . . . . . . . . . . . . . . divide by 32

Putting this into the equation for y, we have ...

  3y = 48.6 -10(4.5)

  3y = 3.6 . . . . . . . . . . simplify

  y = 1.2 . . . . . . . . . . . .divide by 3

The weight of a textbook is 4.5 pounds; the weight of a workbook is 1.2 pounds.

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80