Percentages question

Question

Hi,

Could someone help me with this question? (I believe I have the answer already, but my mom and I are arguing so we need a third opinion :)

There are three blueberries, large, medium, and small. The large is 10% sweeter than the medium, and the medium is 10% sweeter than the smallest. How much sweeter is the largest blueberry than the small? How much more sour is the smallest blueberry than the big?

Answer 1

L = 1.1M

M = 1.1S

L = !.1(1.1S)

L = 1.21S

Large is 21% sweeter than the Small

L = 1.21S

0.826446281L = S

What scale is used to measure sweetness?

Answer 2

Let's give the smallest a sweetness score of 100. Then the medium would have a score of 100 + 10%, or 100 x 1.1 = 110

The largest is 10% sweeter than the medium, so its score is 1.1 x 110 = 121.

Now how to compare the largest with the smallest? 121 - 100 = 21 points higher, but probably better to make a ratio: 121/100 = 1.21 times as sweet or 21% sweeter.

Going in the other direction, the smallest is 100/121, or about 83% as sweet as the largest.

So who wins the argument?