Dr. Johnson’s Shopping Dilemma
Overview of the Purchase
Dr. Johnson visited a shop and bought four items. The prices of the first three items were $1.50, $3.00, and $4.00. Interestingly, the sum of all four prices equaled the product of those same four prices.
Determining the Price of the Fourth Item
To find the price of the fourth item, we will denote it as P. The following equation represents the relationship between the sum and the product of the prices:
1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P
This simplifies to:
8.50 + P = 18.00 x P
Rearranging gives us:
8.50 = 18.00 x P – P
This can be further simplified to:
8.50 = 17.00 x P
To solve for P, we divide both sides by 17.00:
P = 8.50 ÷ 17.00
Thus, the price of the fourth item is:
P = $0.50.