An amount of money is shared among P,Q and R such that for every 3P gets, Q gets 2 and for every 1Q gets, R gets 4. Find P: Q : R

Analyze the question

We are given two ratios and must combine them into one:

• P : Q = 3 : 2 (for every 3 that P gets, Q gets 2)
• Q : R = 1 : 4 (for every 1 that Q gets, R gets 4)

Concept

To join two ratios that share a common term (Q), make Q the same number in both ratios. Use the LCM of Q's values.

Solution

Q appears as 2 in the first ratio and 1 in the second. The LCM of 2 and 1 is 2, so make Q equal to 2 in both.

• P : Q = 3 : 2 (already has Q = 2)
• Q : R = 1 : 4. Multiply both parts by 2 to get 2 : 8.

Now Q is 2 in both ratios, so we can combine them:

P : Q : R = 3 : 2 : 8

Check: Q : R = 2 : 8 = 1 : 4 ✓ and P : Q = 3 : 2 ✓

Answer: E. 3 : 2 : 8

Tip: When combining ratios, always make the shared term equal in both ratios first. Scale the ratio that needs adjusting, multiplying both of its parts by the same number. Then line the ratios up.