If a is 50% larger than c and b is 25% larger than c, then a is
what percent larger than b?
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To find the percentage difference between a and b, we need to compare their sizes. Let's start by understanding the relationship between a, b, and c.
We are given that a is 50% larger than c. This means a = c + 0.5c, or a = 1.5c.
Similarly, we are given that b is 25% larger than c. This means b = c + 0.25c, or b = 1.25c.
To find the percentage difference between a and b, we can use the following formula:
Percentage difference = ((a - b) / b) * 100
Substituting the values of a and b, we have:
Percentage difference = ((1.5c - 1.25c) / (1.25c)) * 100
Simplifying further:
Percentage difference = (0.25c / 1.25c) * 100
Percentage difference = (0.25 / 1.25) * 100
Percentage difference = (1/5) * 100
Percentage difference = 20%
Therefore, a is 20% larger than b.
a=1.5c and b=1.25c, then
c=a/1.5 and c=b/1.25
therefore a/1.5 = b/1.25
a = 1.5b/1.25
a = 1.2 b
so a is 20% larger than b