The weight of 2 science fiction books and 1 autobiography is 5/6w pounds. What is the total weight of 4 of these science fiction books and 2 of these autobiographies?
2science + 1 auto ----> 5/6w pounds
4science + 2 auto
= 2(2science + 1 auto)
= 2(5/6w)
= 5/3w pounds
2 + 1 = 5/6 lbs.
5/6 lbs. + 5/6 lbs. = 10/6 lbs. = 5/3 lbs.
4 + 2 = 5/3 lbs.
2 + 1 = 5/6w lbs.
5/6w lbs. + 5/6w lbs. = 10/6w lbs. = 5/3w lbs.
4 + 2 = 5/3w lbs.
10/12w +8
To find the total weight of 4 science fiction books and 2 autobiographies, we need to first determine the weight of one science fiction book and one autobiography. Let's call the weight of a science fiction book "x" and the weight of an autobiography "y".
Given that the weight of 2 science fiction books and 1 autobiography is 5/6w pounds, we can set up the following equation:
2x + y = 5/6w
To find the weight of one science fiction book, we rearrange the equation:
2x = 5/6w - y
Next, we divide both sides of the equation by 2:
x = (5/6w - y) / 2
Now, we have the weight of one science fiction book in terms of "w" and "y". To find the total weight of 4 science fiction books, we multiply the weight of one science fiction book by 4:
4x = 4 * [(5/6w - y) / 2]
Similarly, to find the total weight of 2 autobiographies, we multiply the weight of one autobiography by 2:
2y = 2 * y
To calculate the total weight of 4 science fiction books and 2 autobiographies, we add the weights together:
Total weight = 4x + 2y
Now we can substitute the expressions we found earlier:
Total weight = 4 * [(5/6w - y) / 2] + 2 * y
Simplifying the expression, we get:
Total weight = (10/6w - 2y) + 2y
The "-2y" and "+2y" terms cancel out, leaving:
Total weight = 10/6w
Therefore, the total weight of 4 science fiction books and 2 autobiographies is 10/6w pounds.