The Correct Answer and Explanation is:
The correct formula is 120 × 1.50.
To understand why this is the correct choice, let’s break down the problem. The question states that Dolphin has “50% more clients than Turtle does.” The formulas provided use the number 120, so we can assume that Turtle has 120 clients.
Calculating a percentage increase involves two steps: finding the amount of the increase and adding it to the original number.
First, we need to determine what 50% of Turtle’s clients is. To do this, we convert the percentage to a decimal (50% = 0.50) and multiply it by Turtle’s client number:
0.50 × 120 = 60
This means Dolphin has 60 more clients than Turtle.
Next, we add this increase to Turtle’s original number of clients to find Dolphin’s total:
120 + 60 = 180
So, Dolphin has 180 clients.
Now let’s examine the formula 120 × 1.50. This formula provides a direct shortcut to the same answer. Multiplying by 1.50 is the same as calculating 150% of the original number. This works because the “1” in 1.50 represents the original 100% (Turtle’s 120 clients), and the “.50” represents the additional 50% increase. The calculation is:
120 × 1.50 = 180
This single step correctly determines the total number of clients Dolphin has.
The other options are incorrect. The formula 120 / 0.50 is equivalent to 120 × 2, which calculates a 100% increase. The formula 120 + (120 × 1.50) would add 150% of the original number back to itself, resulting in a much larger, incorrect total.
