Question

If x: y = 3: 5, find the ratio 3x + 4y: 8x + 5y



2. If x: y = 8: 9, find the ratio (7x – 4y): 3x + 2y.

SOLVE WITH FULL EXPLANATION!!​

Answer 1

$\huge\underline\bold\blue{AnswEr✓}$

Solution:

Given x: y = 3: 5

We can write above equation as

x/y = 3/5

5x = 3y

x = 3y/5

By substituting the value of x in given equation 3x + 4y: 8x + 5y we get,

3x + 4y: 8x + 5y = 3 (3y/5) + 4y: 8 (3y/5) + 5y

= (9y + 20y)/5: (24y + 25y)/5

= 29y/5: 49y/5

= 29y: 49y

= 29: 49

Solution:

Given x: y = 8: 9

We can write above equation as

x/y = 8/9

9x = 8y

x = 8y/9

By substituting the value of x in the given equation (7x – 4y): 3x + 2y we get,

(7x – 4y): 3x + 2y = 7 (8y/9) – 4y: 3 (8y/9) + 2y

= (56y – 36y)/9: 42y/9

= 20y/9: 42y/9

= 20y: 42y

= 20: 42

= 10: 21

Answer 2

SOLUTION

given that

$x :y = 3:5$

$\frac{x}{y} = \frac{3}{5}$

after cross multiplication..

$5x = 3y$

$x = \frac{3y}{5} \\ \\ hence-</p><p> 3x + 4y: 8x \\ + 5y = 3 (3y/5) \\ + 4y: 8 (3y/5) + 5y$

$\frac{9y+ 20y}{5(24y + 25y)} \div 5$

$\frac{9y+ 20y}{5}$

$\frac{29y}{5}: \frac{49y}{5} \\ 29y:49y$

$29:49 \: answer$