Graduation Gift Cards

May 25, 2015

Derrick received a total of 21 gift cards for graduation. He received gift cards in each of four denominations, $25, $50, $75 and $100. The number of $100 gift cards Derrick got was twice the number of $75 gift cards he received. The total value of the $50 gift cards he got exceeded the total combined value of the $25, $75 and $100 gift cards by $100. How many $25 gift cards did Derrick get for graduation?


With the gift card Derrick had left over from his recent birthday, the 22 gift cards have an average value of $50. What is the value of the leftover birthday gift card?


All 21 of the gift cards Derrick received for graduation were for stores at the local mall. He used five gift cards during the mall’s Memorial Day Sale Spectacular. If Derrick used at least two different denominations of gift cards, what is the absolute difference between the greatest and least combined value of his remaining 16 gift cards?