Question

If a : b = 5: 2, find 6a + 2b: 4a + 3b​

Answer 1

To given:

a:b = 5:2

To find:

(6a + 2b) : (4a + 3b)

Solution:

$\sf \: \: a \ratio b = 5 \ratio 2$

$\sf \: let \: \: \frac{a}{b} = \frac{5}{2} = k$

$\sf \: a = 5k \: \: \: \: and \: \: \: b = 2k$

Hence

$\sf \: (6a + 2b) : (4a + 3b)$

$\sf \: \frac{(6a + 2b)}{ (4a + 3b)}$

$\sf \: = \frac{6(5k) + 2(2k)}{ 4(5k) + 3(2k)}$

$\sf \: = \frac{30k + 4k}{ 20k + 6k}$

$\sf \: = \frac{34k}{ 26k}$

$\sf \: = \frac{17}{ 13}$

$\sf \: 17 :13$