Of the 3 numbers, the first is 20% more than the
second which is 20% less than the third, by how much
% is the third number more than the first one?
a) 50% b) 4 1/6% c) 25% d) 8%
Answers
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Answer:
I’ll present two approaches to solving this problem: an algebraic approach and and an applied approach. Let’s start with the applied approach.
We’ll call are through numbers A, B, and C. A is 20% more than C and B is 20% more than C.
Let’s pick an arbitrary number for C. Let’s say C is 100.
If C is 100, then A is 120 and B is 150. We know this because
A = C + 20% of C = 120% of C = 1.2C
and because C is 100, 1.2C is 120. The same logic applies for B being 150.
To figure out what percentage the first number (A) is of the second (B), it’s a simple fraction, A/B, converted to a decimal by dividing.
120/150 = 0.8, which, when expressed as a percentage, is 80%.
You can try this with any C. Let’s use 15 to see if we get the same answer.
C = 30
A = 1.2 * C = 36
B = 1.5 * C = 45
A / B = 36/45 = 0.8, or 80%
It works even when the numbers are decimals!
C = 18
A = 1.2 * C = 21.6
B = 1.5 * C = 27
A / B = 21.6 / 27 = 0.8, or 80%
So, practically, it appears that, for any chosen C, A is always 80% of B. Let’s see if we can make that into an equation so as not to rely on a few examples.
We know that A is always 1.2 * C. I’ll write that as 1.2C
We know that B is always 1.2 * C, which I’ll write as 1.5C
As above, to figure out what percentage A is of B, we make it into a fraction.
A / B = 1.2C / 1.5C
Now, there’s a C on the top AND bottom of our fraction, so we can cancel them out. We’re left with this:
A / B = 1.2 / 1.5 = 0.8, or 80%