Sarah, Ivory and Tammy had 810 coins. Ivory won some of the coins from Sarah and as a result, Ivory's coins increased by 25%. Tammy then won some coins from Ivory and Tammy's coins increased by 80%. Finally, Tammy lost some of her coins to Sarah and Sarah's coins increased by 20%. In the end, they realised that they each had an equal number of coins. How many percent less did Sarah have in the end than what she had at first? Correct your answer to 1 decimal place.

Sarah	Ivory	Tammy
810
	4 u
- 1 u	+ 1 u
	5 u
		5 p
	- 4 p	+ 4 p
		9 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

25% = ²⁵₁₀₀ = ¹₄
80% = ⁸⁰₁₀₀ = ⁴₅
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 810

1 group = 810 ÷ 3 = 270

1 group = 6 boxes
6 boxes = 270

1 box = 270 ÷ 6 = 45

1 group + 1 box = 9 p
270 + 45 = 9 p
9 p = 315

1 p = 315 ÷ 9 = 35

4 p = 4 x 35 = 140

1 group + 4 p = 5 u
270 + 140 = 5 u
5 u = 410

1 u = 410 ÷ 5 = 82

Number of coins that Sarah had at first
= 5 boxes + 1 u
= (5 x 45) + 82
= 225 + 82
= 307

Percent that Sarah had less in the end than at first
= ^{307 - 270}₃₀₇ x 100%
≈ 12.1%

Answer(s): 12.1%