Question

(i) If a : b = 8 : 9, find the ratio of
(7a - 4b): (3a + 2b).
(ii) If a : b 5 : 3. show that
(5a + 8b) : (6a - 7b) = 49 : 9.
ICSE
1​

Answer 1

Step-by-step explanation:

(7*8-4*9):(3*8+2*9)

56-36/24+18

20/42= 10:21

(5*5+8*3): (6*5-7*3)

25+24/30-21= 49/9

Answer 2

Answer:

So, we have the question like this

if a/b = 8/9 it means that by cross multiplying we have,

9a=8b this also means that,

b=9a/8 equation (1)

now we have to solve the given ratio,

we have,

(7a - 4b) : (3a + 2b)

from equation (1) we have b= 9a/8

substituting it we have,

7a - 4(9a/8) : 3a + 2(9a/8)

= 7a - 36a/8 : 3a + 18a/8

taking 8 as LCM we have,

(56a - 36a)/8 : (24a +18a)/8

here we have 8 both in numerator as well as denominator so we can just cancel it out,

now we have,

20a : 42a

same as the above step we can cancel out a

we have,

20 : 42

by simplifying we have,

10 : 21

this was part 1 solved

for part 2 we do the same process

a:b = 5:3 it implies a/b = 5/3 it implies b = 3a/5

substituting in given we have,

5a + 8(3a/5) : 6a - 7(3a/5)

= 5a + 24a/5 : 6a - 21 a/ 5

= 25a + 24a : 30a -21 a

= 49a : 9a

= 49:9

I hope it helped ^^

see ya!