Shareholders' Equity (Details) - USD ($) $ / shares in Units, $ in Millions		3 Months Ended		9 Months Ended
	May 25, 2022	Apr. 30, 2022	Apr. 30, 2021	Apr. 30, 2022	Apr. 30, 2021
Stockholders' Equity Note [Abstract]
Number of shares authorized to be repurchased (in shares)		13,000,000		13,000,000
Stock repurchased during the period (in shares)				2,500,000
Stock repurchased during the period				$ 153.7	$ 78.7
Shares with remaining authorization for repurchase under stock repurchase plan (in shares)		5,800,000		5,800,000
Dividends paid per share (in usd per share)		$ 0.22	$ 0.21	$ 0.66	$ 0.63
Schedule of Equity Method Investments [Line Items]
Dividends, per share (in usd per share)				$ 0.44	$ 0.42
Subsequent Event
Schedule of Equity Method Investments [Line Items]
Dividends, per share (in usd per share)	$ 0.23