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Asked by Jodie

There are 3 rectangles A B and C. The area of rectangle B is 10% greater then the area of rectangle A. The area of rectangle C is 10% greater then the area of rectangle B. By what percentage is the area of rectangle C greater then rectangle A?

I have written a full algebraic solution to see this, but there is also a quick way of thinking this through at the bottom. Let's take the area of rectangle A and let us call it - a. Similarly we will call area of rectangle B - b and the same for rectangle C - c. In the question we know area b is 10% bigger then area a. So we can write. <Eq 1> b = 1.1a (or we could write 100a = 110b if we want to work with the percentages - these are equivalent) <Eq 2> Similarly we know: c = 1.1b (or 100c = 110b) Let's rearrange this so we can substitute into <Eq 1> For this we want b by itself on a side. Therefore let's divide both sides by 1.1. c / 1.1 = b Now let's substitute b in to <Eq 1> to allow us to relate a and c. c / 1.1 = 1.1a Multiply both sides by 1.1 c = (1.1 x 1.1)a c = 1.21a To use percentages let's multiply 1.21 So 100% of c - the full area of c is equal to 121% of shape a. The area has increased by 21%. Instead of writing the full algebraic solution, you could think of it as shape a increasing by 10% and then this increasing by 10%. In decimal this is a 1.1 squared increase (1.21).

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Alexander Stronach
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