Calculate Black Chairs: Finding 40 Percent of 125 Using Complementary Percentages

Question

There are 125 chairs in a room. 60% of the chairs are white , while the rest are black. How many black chairs are there?

Video Solution

Solution Steps

00:00 Establish the number of black chairs
00:05 Subtract the percentage of white chairs from the whole in order to determine the percentage of blacks
00:15 This is the percentage of black chairs
00:20 Use the formula to convert percentages to fractions
00:26 Apply this formula to our exercise
00:31 Multiply this fraction by the whole in order to identify the total number of black chairs
00:46 Break down 40 into factors of 4 and 10, and 125 into factors of 25 and 5
00:51 Break down 100 into factors of 25 and 4
01:01 Reduce wherever possible
01:10 This is the solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Calculate the number of white chairs from the given percentage.
  • Step 2: Determine the number of black chairs by subtraction.

Let's work through each step:

Step 1: Calculate the number of white chairs.
The total number of chairs is 125. Since 60% of these chairs are white, we calculate the number of white chairs as follows:
White chairs=125×0.60=75\text{White chairs} = 125 \times 0.60 = 75

Step 2: Determine the number of black chairs.
Subtract the number of white chairs from the total number of chairs to find the number of black chairs:
Black chairs=12575=50\text{Black chairs} = 125 - 75 = 50

Therefore, the number of black chairs is 50.

Answer

50