Alex bought some baseball cards for 50 cents each and half as many of some more valuable cards for a 1.50 each. He spent a total of 80 dollars. How many of 1.50 cards did he buy?

There are 32 cards bought for 1.50 each

x is the number of cards bought for 50 cents; x = 64

x/2 is the number of cards bought for 1.50 each; x/2 = 64/2 = 32

0.50x + (1.50 * x/2) = 80

0.50x + 1.50x / 2 = 80

2 (0.50x + 1.50x / 2) = 80 * 2

x + 1.50x = 160

2.50x = 160

2.50x / 2.50 = 160 / 2.50

x = 64

To check: Substitute x by its value

0.50 (64) + (1.50 * 64/2) = 80

32 + (1.50 * 32) = 80

32 + 48 = 80

80 = 80