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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?

Sagot :

Mlcparra16idn
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.




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