If a is 50 percent larger than c and b is 25 percent larger than c, then a is what precent larger than b?
a/c = 1.5
b/c = 1.25
a/b = (a/c)/(b/c) = 1.20
a is 20% greater than b
Thank you, but how did you figure this out?
To determine the percentage that a is larger than b, we need to compare their values relative to c.
Let's assume the value of c is 100. Since a is 50 percent larger than c, we calculate it as follows:
a = c + (50/100) * c
a = c + 0.5c
a = 1.5c
Now, we determine the value of b, which is 25 percent larger than c:
b = c + (25/100) * c
b = c + 0.25c
b = 1.25c
To find the percentage that a is larger than b, we can calculate the percentage increase:
Percentage increase = ((New value - Old value) / Old value) * 100
Percentage increase = ((1.5c - 1.25c) / 1.25c) * 100
Simplifying the equation, we get:
Percentage increase = (0.25c / 1.25c) * 100
The c cancels out, resulting in:
Percentage increase = 0.2 * 100
Percentage increase = 20%
Therefore, we can conclude that a is 20 percent larger than b.