Bunuel wrote:

In store A there are 10 pairs of pants for every 40 store B has. The price ratio between the pants in store B and the pants in store A is 3:4. If all the pants were sold in both places until the stock ran out, what is the ratio between the total amount stores A earned to the total amount store B earned?

A. 3:16.

B. 2:3.

C. 1:3.

D. 3:4.

E. 2:5.

This problem's wrinkles are that the ratios switch, and the wording of the first sentence might be confusing.

Quantity ratio (for every 40 pairs that B has, A has 10 pairs):

\(\frac{A}{B}\) = \(\frac{10x}{40x}\) = \(\frac{1x}{4x}\)

A has 1x or 1

B has 4x or 4*

Price ratio ("price ratio between pants in B and pants A is 3:4") - I keep the same variables as those on the top and bottom of the first ratio

\(\frac{A}{B}\) = \(\frac{4y}{3y}\)

A charges 4y or 4

B charges 3y or 3

All pants are sold. What is ratio between the total amount (quantity * price) that A earned to total amount B earned?

A earned 1 * 4 = 4

B earned 4 * 3 = 12

Ratio of A's total earnings to B's total earnings:

\(\frac{4}{12}\) = \(\frac{1}{3}\) = 1:3

Answer C

*(x and y are ratio multipliers; as long as the ratio stays the same when solving at the end, you can assume values such as 1 and 4, and 4 and 3)

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"