Question

Given that a:b:= 75: 120: 132.
i.
Simplify b:c

Answer 1

Answer:

a:b:c = 25:40:44 (simplified)

b:a = 8:5 (simplified)

b:c = 10:11 (simplified)

Step-by-step explanation:

a:b:c ---> 75:120:132

SIMPLIFYING a:b:c :

First, find out the HCF of 75, 120 and 132.

120 and 75 :

120 = 75*1 + 45

=> 75 = 45*1 + 30

=> 45 = 30*1 + 15

=> 30 = 15*2 + 0

Now, 15 and 132 :

132 = 15*8 + 12

=> 15 = 12*1 + 3

=> 12 = 3*4 + 0

Thus, HCF of 75, 120 and 132 is 3.

Now divide all three nos. by 3.

75/3: 120/3: 132/3

=> 25:40:44 is the simplified form of 75:120:132.

FINDING b:a :

As a:b:c = 25:40:44,

b:a = 40:25 => 8:5       (Dividing by 5)

FINDING b:c :

As a:b:c = 25:40:44,

b:c = 40:44 => 10:11       (Dividing by 4)

Answer 2

Answer:-

Given

3a = 5b and 6b = 7c

TO DETERMINE

The value of a : b : c

EVALUATION

Here it is given that 3a = 5b and 6b = 7c

3a = 5b gives

a = $\frac{5b}{3}$

6b = 7c gives

c = $\frac{6b}{7}$

Now

a : b : c

= $\frac{5b}{3}$ : b : $\frac{6b}{7}$

= $\frac{5}{3}$ : 1 : $\frac{6}{7}$

= $( \frac{5}{3}$ × 21$)$ : (1 × 21) :$(\frac{6}{7}$ × 21$)$

= 35 : 21 : 18