Question

If a : b = 3 : 11 then (15a – 3b) : (9a + 5b) is equal to ______.

Options

• 35 : 6

• 6 : 35

• 6 : 41

• 41 : 6

Answer 1

If a : b = 3 : 11 then (15a – 3b) : (9a + 5b) is equal to 6 : 41.

Explanation:

a : b = 3 : 11

`a/b = 3/11`

Now,

`(15a - 3b)/(9a + 5b)`

we can divide every term in the expression by b,

= `((15a - 3b)/b)/((9a + 5b)/b)`

= `(15(a/b) - 3)/(9(a/b) + 5)`

= `(15(3/11) - 3)/(9(3/11) + 5)`

= `(45/11 -3)/(27/11 + 5)`

= `((45 - 3 xx 11)/11)/((27 + 5 xx 11)/11)`

= `((45 - 33)/11)/((27 + 55)/11)`

= `(12/11)/(82/11)`

= `12/82`

= `6/41`