Question

If P: Q = 6:11, Q: R = 5:4, and R: 5 = 9: 7, find P: Q: R : S.

• A. 270:495:396:308
• B. 6:11:4:7
• C. 30:55:44:35
• D. 270:396:495:308

Answer 1

Answer:

A. 270:495:396:308

Given:

• (P:Q = 6:11)

• (Q:R = 5:4)

• (R:S = 9:7)

We need to find (P:Q:R:S).

Step 1: Equalize (Q)

• (P:Q = 6:11)

• (Q:R = 5:4)

LCM of 11 and 5 = 55.

Multiply:

• (P:Q = 6:11) by 5 → 30:55

• (Q:R = 5:4) by 11 → 55:44

So,
P:Q:R = 30:55:44

Step 2: Equalize (R)

• Current (R = 44)

• Given (R:S = 9:7)

LCM of 44 and 9 = 396.

Multiply:

• (30:55:44) by 9 → 270:495:396

• (9:7) by 44 → 396:308

Therefore,

$\boxed{P:Q:R:S = 270:495:396:308}$

This ratio cannot be simplified further.

Answer: $(\boxed{270:495:396:308})$