Dr. Johnson’s Shopping Dilemma

Items Purchased

Dr. Johnson visited a shop and bought four items. The costs of three of these items were as follows: $1.50, $3.00, and $4.00.

The Curiosity of Prices

Interestingly, the total of the four prices equaled the product of those same prices. The task is to determine the price of the fourth item.

Calculating the Missing Price

Let’s denote the unknown price as P. We can express the situation with the following equation:

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 the equation gives:

8.50 = 18.00 x P – P

Thus:

8.50 = 17.00 x P

To find P, we divide both sides by 17.00:

P = 8.50 ÷ 17.00

Conclusion

The price of the fourth item is $0.50.