Jawab:

The original price of p is $45.

Penjelasan dengan langkah-langkah:

Notes:

I don’t know whether it is “socks” or “stocks”. Please re-read your question. So, I will just use p and q.

Given that the ratio of p and q is 5 : 7, we can get:

p : q = 5 : 7

q = (7/5)p     .....(i)

The price of p is increased by $12:

P = p + $12    .....(ii)

The price of q is decreased by $6:

Q = q – $6     .....(iii)

Updated prices of both p and q are the same in the end.

So, (ii) = (iii)  ⇒ P = Q

⇔ p + $12 = q – $6

Plug the value of q we got from (i).

⇔ p + $12 = (7/5)p – $6

Multiply both sides by 5.

⇔ 5p + 5($12) = 7p – 5($6)

⇔ 5p + $60 = 7p – $30

Substract 5p from both sides.

⇔ 5p + $60 – 5p = 7p – $30 – 5p

⇔ $60 = 2p – $30

Add $30 to both sides.

⇔ $60 + $30 = 2p – $30 + $30

⇔ $90 = 2p

Switch sides.

⇔ 2p = $90

Divide both sides by 2.

⇔ 2p/2 = $90/2

⇔ p = $45

Therefore, the original price of p is $45.