When the price of an article is reduced by 5/8 of its former value, the number of article sold is increased to 32/27 of the original amount. The present daily revenues is what fraction of the original?
Well, if we start off with some original humor-filled revenue, let's call it the "Moola Machine," and then reduce the price by 5/8, we might end up with the "Cheapskate Cash Dispenser."
Now, when the price drops, people go crazy, and the number of articles sold increases to 32/27 of the original amount. Let's call these enthusiastic customers "Bargain Bandits."
So, here's the equation: Cheapskate Cash Dispenser x Bargain Bandits = Present Daily Revenues.
Now, we need to find out what fraction of the original revenue the present daily revenue represents. Let's call this fraction the "Reduced Riches Ratio."
To calculate the Reduced Riches Ratio, we need to divide the Present Daily Revenues by the Original Revenue. So, to put on our mathematical clown shoes and crunch the numbers, we find:
Reduced Riches Ratio = (Cheapskate Cash Dispenser x Bargain Bandits) / Moola Machine.
And there you have it, my friend! The Reduced Riches Ratio calculates how much our present daily revenue is in comparison to the original revenue. Isn't math funny?
To find the present daily revenue as a fraction of the original, we need to consider the changes in both price and quantity sold.
Let's assume the original price of the article is represented by "P" and the original quantity sold is represented by "Q". Therefore, the original daily revenue can be represented as P * Q.
According to the information given, the price of the article is reduced by 5/8 of its former value. So the new price, denoted as "P'", can be calculated as:
P' = P - (5/8)P
= (8/8)P - (5/8)P
= (3/8)P
The number of articles sold is increased to 32/27 of the original amount. So the new quantity sold, denoted as "Q'", can be calculated as:
Q' = (32/27)Q
The present daily revenue, denoted as "R'", can be calculated as:
R' = P' * Q'
= (3/8)P * (32/27)Q
= (3 * 32 / 8 * 27) * P * Q
= 96/216 * P * Q
= 8/18 * P * Q
= 4/9 * P * Q
Therefore, the present daily revenue is 4/9 of the original daily revenue.
To find out the present daily revenue as a fraction of the original, we need to consider the changes in both the price and the quantity of articles sold.
Let's assume that the original price of the article was "P" and the original quantity sold was "Q". Therefore, the original daily revenue would be calculated as:
Original Daily Revenue = Original Price x Original Quantity = P x Q
Now, the price of the article is reduced by 5/8 of its former value, which can be expressed as:
New Price = Original Price - (5/8) x Original Price = (3/8) x Original Price
Next, the number of articles sold is increased to 32/27 of the original amount:
New Quantity Sold = (32/27) x Original Quantity
Now, to calculate the present daily revenue, we multiply the new price by the new quantity sold:
Present Daily Revenue = New Price x New Quantity Sold = (3/8) x Original Price x (32/27) x Original Quantity
Simplifying this expression, we get:
Present Daily Revenue = (3/8) x (32/27) x Original Price x Original Quantity
Now, we can see that the fraction of the present daily revenue to the original daily revenue can be represented as:
Present Daily Revenue / Original Daily Revenue = [(3/8) x (32/27) x Original Price x Original Quantity] / (P x Q)
Simplifying this expression, we find:
Present Daily Revenue / Original Daily Revenue = (3/8) x (32/27)
To find the fraction in its simplest form, we can simplify the given expression further:
Present Daily Revenue / Original Daily Revenue = (3/8) x (4/3) = 12/24
Therefore, the present daily revenue is equal to 12/24, which can be simplified to 1/2, or one-half, of the original daily revenue.
n sold originally at p
32 n/27 sold later at 5 p/8
original rev = n p
final rev = (32/27)(5/8) n p
so
(32/27) (5/8) = 20/27