Answered

Makahanap ng mga solusyon sa iyong mga problema sa tulong ng mga eksperto ng IDNStudy.com. Ang aming mga eksperto ay nagbibigay ng mabilis at eksaktong sagot upang tulungan kang maunawaan at malutas ang anumang problema.

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.