Alan bought a total of 20 game cards, some of which cost $0.25 each and some of which cost $0.15 each. If Alan spent $4.20 to buy the cards, how many cards of each type did he buy?

Start by assigning X as the number of cards that cost $0.25 each and Y as the number of cards that cost $0.15. Knowing that the total number of cards equals 20, we can write the equation: X + Y = 20 Now we can say that the X cards cost: 0.25 X And the Y cards cost: 0.15 Y If the total cost for the cards is $4.20, we can say: 0.25 X + 0.15 Y = 4.2 Now solve the system of equations: X + Y = 20 0.25 X + 0.15 Y = 4.2 The first equation gives Y = 20 - X. Substitute Y by 20 - X in the second equation and solve 0.25 X + 0.15 (20 - X) = 4.2 X(0.25 - 0.15) + 3 = 4.2 0.1 X = 1.2 X = 12 and Y = 20 - 12 = 8

Asked by Tom Tennant · Last updated 5 years ago · 1.6K views · SOURCE