In September, Bryan gave his wife, Rachel, $8000 for household expenditure. Rachel spent 50% of the sum on rental, 20% on food and saved the rest. In October, Bryan reduced the sum he gave to Rachel. Rachel spent the same amount on rental and reduced the amount she spent on food by 10%. She saved the remaining 20% of the sum given to her in October. By what percentage was the sum given to Rachel reduced by?

	Rental	Food	Savings	Total
Before	50%	20%	30%	$8000
Change		- 2%	- ?	- ?
After	50%	18%
Comparing the amounts spent in October	80 u		20 u	100 u

Amount that Bryan saved in percent
= 100% - 50% - 20%
= 30%

Amount that Bryan reduced on food in percent
= 10% x 20%
= ¹⁰₁₀₀ x 20
= 2%

Total amount that Bryan spent on rental and food in percent
= 50% + 18%
= 68%

100% → 8000

1% → 8000 ÷ 100 = 80

68% → 68 x  80 = 5440

The total amount that Bryan spent on rental and food is repeated. 

80 u = 68% 

80 u = 5440

1 u = 5440 ÷ 80 = 68

Amount that Bryan gave to Rachel in October
= 100 u
= 100 x 68
= $6800

Amount that Rachel received less from Bryan from September to October
= 8000 - 6800
= $1200

Percentage that the sum given to Rachel was reduced by from September to October
= ¹²⁰⁰₈₀₀₀ x 100%
= 15%

Answer(s): 15%