Let us represent ...
the mass of the box be x; and
the mass of each book be y
We know the following:
x + (3/4)(36)y = x + 36y - 75 ... [1]
y = (5/7)x ... [2]
Let us first focus on [1]:
x + (3/4)(36)y = x + 36y - 75
x + 27y = x + 36y - 75
We subtract x from both sides
27y = 36y - 75
We then add 75 to both sides
27y + 75 = 36y
Lastly, we subract 27y from both sides
75 = 36y - 27y
75 = 9y
25/3 = y
We then substitute the value of y to [2]:
25/3 = (5/7)x
We multiply 7/5 to both sides
(25/3)(7/5) = x
35/3 = x
So now that we have the mass of the box and a book we get the total mass of all:
x + 36y = 35/3 + 36(25/3) = 35/3 + 300 = 11 2/3 + 300 = 311 2/3 kg
Final answer: The total mass of the box and the 36 books is 311 2/3 kg.
