Dany bought a total of 22 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?	Options:
A) 4
B) 10
C) 7
D) 8
E) 13
Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 22. Hence   X + Y = 22   If X is the number of cards at $0.25, then the X cards cost   0.25 X   If Y is the number of cards at $0.15, then the Y cards cost   0.15 Y   The total cost of the X cards and the the Y cards is known to be $4.2 and also given by   0.25 X + 0.15 Y = 4.2   We now need to solve the system of equations   X + Y = 22   0.25 X + 0.15 Y = 4.2   The first equation gives Y = 22 - X. Substitute y by 22 - x in the second equation and solve   0.25 X + 0.15 (22 - X) = 4.2   X(0.25 - 0.15) + 3.3 = 4.2   0.1 X = 0.9   X = 9 and Y = 22 - 9= 
<gadget id="calculator">22 - 9</gadget>
<output>13</output>
13   correct answer 13
<result>E</result>
Dany bought a total of 22 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?