A self-serve frozen yogurt restaurant charges its customers according to the weight of their filled frozen yogurt cup. So, the amount they charge is directly proportional to the weight of the purchase. If they charge $5.04 for a 12-ounce cup, how much do they charge for a cup weighing 8 ounces?

If the price of the yogurt is directly proportional to the weight of the purchase, then it can be expressed as:

Price of yogurt = weight of purchase

With the given above, it can be further expressed as:

$5.04 = 12 oz

These can be expressed in ratio form, which is:

5.04/12

Thus, if the cup weighs 8 oz and we don't know how much it costs, then the ratio should be:

n = 8 oz, or in fractions:

n/8

After this, simply equate the two and cross multiply.

5.04 / 12 = n/8

5.04 (8) = 12n

40.32 = 12n

Then solve for n:

40.32 / 12 = 12n/12

n = 3.36.

Thus, the 8 oz. cup of yogurt costs $3.36.