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A box contains 36 similar books. the total mass of the box together with 3/4 of the books is 75 kg lighter than that of the box with all the books. the

mass of eaxh book is 5/7 times the mass of the box. what is the total mass of the box and its contents?

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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.

Mass of the box: x Mass of each book: ⁵/₇ x Total books: 36 Total Mass of 36 books: (⁵/₇x) (36) = ¹⁸⁰/₇ x Mass of 3/4 of total books: (³/₄)(¹⁸⁰/₇ x) = ¹³⁵/₇ x

Equation: x + ¹³⁵/₇ x = x + ¹⁸⁰/₇x - 75

x + ¹³⁵/₇ x - x - ¹⁸⁰/₇ x = -75

-180x/7 + 135x/7 = - 175

-180x + 135x = -75 (7)

-45x = -525

-45x/-45 = -525/-45

x = 525/9 or 35/3

The mass of the box is 35/3 kg or 11.67 kg.

Total mass of the books: (5/7) (35/3) x 36 = (25/3) (36) = 300 kg.

Box with Total books: 35/3 + 300 = 311 ²/₃ kg. or 311.67 kg.

Final Answer: The mass of the box and its contents is 311 ²/₃ kg or 311.67 kg.