Agrocery store gives away a $10 gift card to every 25th customer and a $20 gift card to every 60th customer. after this customer receives both gift cards, what is the total amount in gift cards that the store has given away

Most of the time the same customer is not allowed to receive two separate prizes.  Let's assume it is possible (because it says so).

The LCM of 25 and 60 is 300  (25=5^2, 60=2^2*3*5), so LCM = 60*5=300).
Store has given out 300/25=12 $10 gift cards.
Store has given out 300/60=5 $20 gift cards.
After the lucky customer has given out the above prizes, total amount given out is:
total=12*$10+5*$20=$120+$100=$220.