The Correct Answer and Explanation is:
The correct formula to determine the number of clients Dolphin Inc. has is: 120 * 1.50
Here is a detailed explanation of how to arrive at this formula.
The problem states that Dolphin Inc. has 50% more clients than Turtle Inc. This is a crucial detail. It does not mean Dolphin has 50% of Turtle’s clients; it means Dolphin has all of Turtle’s clients plus an additional 50%. We can think of Turtle’s client base as the starting point, which represents 100%.
To find the total number of clients for Dolphin, we need to calculate what 100% plus an additional 50% represents.
100% (Turtle’s original amount) + 50% (the additional amount) = 150%
So, Dolphin Inc. has a number of clients equivalent to 150% of Turtle Inc.’s client base. To use this percentage in a mathematical formula, we must convert it into a decimal. We do this by dividing the percentage by 100.
150 / 100 = 1.50
This value, 1.50, is the multiplier we use on Turtle’s original number of clients to find Dolphin’s total. Since Turtle Inc. has 120 clients, the formula becomes:
120 * 1.50 = 180
Therefore, Dolphin Inc. has 180 clients.
An alternative way to formulate this is a two step process. First, calculate the “more” part by finding 50% of 120 (0.50 * 120 = 60). Second, add this result back to the original number (120 + 60 = 180). This can be written as a single formula: 120 + (0.50 * 120). Both formulas are mathematically equivalent and yield the correct answer, but using the 1.50 multiplier is a more direct and efficient method for calculating a percentage increase.
