(p + 2q)/p = 7/3

Multiply both sides by 3,

3(p + 2q)/p = 7

Multiply both sides by p,

3(p + 2q) = 7p

3p + 3(2q) = 7p

3p + 6q = 7p

6q = 7p - 3p

6q = 4p

Divide both sides by q,

6 = 4p/q

Divide both sides by 4,

6/4 = p/q

3/2 = p/q

Shorter working once you have understood the previous one :


(p + 2q)/p = 7/3

cross multiply,
(basically combining the 2 separate steps in the previous working into 1)

3(p+2q) = 7p

3p + 6q = 7p

6q = 4p

Cross divide,

p/q = 6/4

p/q = 3/2

Thank you J. I also got the same answer but the answer key is 1/2. I will stick to this answer. Thank you.

Alternative :


① (p + 2q)/p = 7/3

② p/p + 2q/p = 7/3

③ 1 + 2q/p = 7/3

④ 1 + 2q/p - 1 = 7/3 - 1

⑤ 2q/p = 4/3

⑥ 2q/p ÷ 2 = 4/3 ÷ 2

⑦ q/p = 2/3

⑧ 3q = 2p (doing cross multiplication)

⑨ p/q = 3/2 (doing cross division)

You can skip writing steps ②, ④, ⑥, ⑧ once you understand the working.

From ⑦ to ⑨, we can tell the ratio of q to p is 2 : 3.

So p is 3/2 of q and thus p/q = 3/2.

Simply invert the fraction.

Welcome.