5/y + 7/x = 24

12/y + 2/x = 24, find the ratio of x to y.

Step-by-step explanation:

5/y + 7/x = 24 ... (1)

12/y + 2/x = 24 ... (2)

Let 1/y = a and 1/x = b

5a + 7b = 24 ... (3)

12a + 2b = 24 ... (4)

Multiply (3) by 2 and (4) by 7

10a + 14b = 48 ... (5)

84a + 14b = 168 ... (6)

Substracting (5) from (6)

84a - 10a = 168 - 48

74a = 120

a = 120/74

a = 60/37

Putting a = 60/37 in (3)

5a + 7b = 24

5 (60/37) + 7b = 24

300/37 + 7b = 24

Multiply each term 37

300 + 259b = 888

259b = 888 - 300

259b = 588

b = 588/259

And a = 1/y

60/37 = 1/y

Cross multiply

60y = 37

y = 37/60

Also

b = 1/x

588/259 = 1/x

Cross multiply

588x = 259

x = 259/588