In February, Luke gave his wife, Olivia, $8000 for household expenditure. Olivia spent 50% of the sum on rental, 30% on food and saved the rest. In March, Luke reduced the sum he gave to Olivia. Olivia spent the same amount on rental and reduced the amount she spent on food by 20%. She saved the remaining 20% of the sum given to her in March. By what percentage was the sum given to Olivia reduced by?

	Rental	Food	Savings	Total
Before	50%	30%	20%	$8000
Change		- 6%	- ?	- ?
After	50%	24%
Comparing the amounts spent in March	80 u		20 u	100 u

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

Amount that Luke reduced on food in percent
= 20% x 30%
= ²⁰₁₀₀ x 30
= 6%

Total amount that Luke spent on rental and food in percent
= 50% + 24%
= 74%

100% → 8000

1% → 8000 ÷ 100 = 80

74% → 74 x  80 = 5920

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

80 u = 74% 

80 u = 5920

1 u = 5920 ÷ 80 = 74

Amount that Luke gave to Olivia in March
= 100 u
= 100 x 74
= $7400

Amount that Olivia received less from Luke from February to March
= 8000 - 7400
= $600

Percentage that the sum given to Olivia was reduced by from February to March
= ⁶⁰⁰₈₀₀₀ x 100%
= 7.5%

Answer(s): 7.5%