Answer:
- Physics Text: 5.7 lb
- Physics Workbook: 1.2 lb
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.
