The number a exceeds the number b by 50 percent. By what percent is the number b smaller than the number a?
a = b + 0.50b = 1.5 b
b = a/1.5 = 2/3 a
so, b is 1/3 less than a, or 33.3% less
i dunno. dont even ask.
To find the percentage by which the number b is smaller than the number a, we can use the formula:
Percentage = (Difference / Original number) * 100
First, let's determine the difference between the two numbers, a and b.
Since the statement says that "a exceeds b by 50 percent," it means that a is 50 percent greater than b. Mathematically, we can express this as:
a = b + (50% of b)
To calculate this, we need to convert 50% to its decimal form, which is 0.5.
a = b + (0.5 * b)
a = 1.5 * b
Now, let's find the difference between the two numbers:
Difference = a - b
Difference = 1.5 * b - b
Difference = 0.5 * b
Now that we have the difference, we can calculate the percentage by dividing the difference by the original number (b) and then multiplying by 100:
Percentage = (Difference / Original number) * 100
Percentage = (0.5 * b / b) * 100
Percentage = 0.5 * 100
Percentage = 50%
So, the number b is smaller than the number a by 50 percent.