Q#.1,2. 108 identical books have a mass of 30 kg. a) the mass of 150 such books

 

New Secondary mathematics 

Students course book 2                             class> VII

Direct and Inverse proportions

Exercise 1A

1.  108 identical books have a mass of 30 kg find

Let book= X

 Mass = Y

If the number of books increases the mass of books will also increase so X is  directly proportional to the Y. The equation will be

X ∝ Y    (symbol of direct relation)

Y = KX (Where K is constant)

30 = K × 108

K= 30/108

 Y= 30/80X

i)The mass of 150 such books

Solution.

Y = KX

Y = 30/108×150

Y = 125/3

Y = 41 2/3

(mass of 150 books is 41 2/3 Kg)

 

ii. The number of such books that have a mass of 20 kg

 

Y= KX

20 = 30/108×X

X = 20 ×108/30

X = 2 × 108/3

X = 2 × 36

X = 72  (72 have the mass of 20 Kg)

 

2. In a bookstore 60 identical books occupy a length of 1.5 m on a shelf find

 

Solution:

Let book= X

 length of Shelf = Y

If the number of books increases the length of Shelf will also increase so X is  directly proportional to the Y. The equation will be

X ∝ Y    (symbol of direct relation)

Y = KX (Where K is constant)

1.5 = K × 60

K = 1.5 ÷ 60

K = 0.025

 

I) the length occupied by 50 such books on a shelf

Y = KX

Y= 0.025 × 50

Y= 1.25 m

 

ii) the number of such books needed to completely occupy a shelf that is 80 cm long

 80 cm = 0.8m (1 meter is equal to 100 cm)

Y = KX

0.8 = 0.025 × X

X = 0.8 ÷ 0.025

X = 32 books