If a is 50% larger than c and b is 25% larger than c, then a is
what percent larger than b?
(a) 20%
(b) 25%
(c) 50%
(d) 100%
(e) 200%
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im confused on how to go about the problem. that's y i need help on how to start.
To determine how much larger a is than b, we need to compare the difference between their values.
Let's start by representing the size of c as x. If a is 50% larger than c, then a is equal to c + 50% of c. In other words, a = c + 0.5c = 1.5c.
Similarly, if b is 25% larger than c, then b is equal to c + 25% of c. In other words, b = c + 0.25c = 1.25c.
Now, we can compare a and b:
a is 1.5c, and b is 1.25c.
To determine what percent larger a is than b, we need to find the ratio of the difference between a and b to the value of b. The formula for this is: (a - b) / b * 100.
Substituting the values, we have: ((1.5c - 1.25c) / 1.25c) * 100.
Simplifying this expression, we get: (0.25c / 1.25c) * 100 = 0.2 * 100 = 20%.
Therefore, a is 20% larger than b.
The correct answer is (a) 20%.