Karen buys enough cans of soda to last her 30 days. The next time Karen is at the store, she sees that the price of cans of soda is on-sale for 25% less than their original value. If Karen spends the exact same amount on cans of soda, how long will the new on-sale supply last her

40 days

Explanation:

if Karen spent X amount of dollars in soda cans that last for 30 days, and the next time the price of each soda can is reduced to 0.75X, then her new purchase should last her = 30 days / 0.75 = 40 days.

For example, each soda can costs $1 and Karen buys 2 cans per day = 60 cans $1 = $60. if the new price of each can is $0.75, with $60 she will be able to purchase 80 cans which should last her 40 days ( = 80 cans / 2 cans per day).