Luke, Michael, Carl and Gabriel paid a total of $264 for a present. Gabriel paid ²₉ of what the rest paid. Luke paid 50% of what the rest paid. Michael and Carl paid an equal amount of money. How much did Carl pay?

Luke	Michael	Carl	Gabriel	Total
9x3			2x3	11x3
1x11	2x11			3x11
	1	1
11 u	8 u	8 u	6 u	33 u

50%= ⁵⁰₁₀₀= ¹₂
Luke's share : Total share = 1 : 2

The total amount paid for the present is repeated.  Make the total amount the same.  LCM of 11 and 3 is 33.

Amount that Michael, Carl and Gabriel paid = 22 u

Amount that Michael and Carl paid
= 22 u - 6 u
= 16 u

The amount that Michael and Carl each paid is the same.

Amount that Michael and Carl each paid
= 16 u ÷ 2
= 8 u

Cost of the present = 33 u

33 u = 264

1 u = 264 ÷ 33 = 8

Amount that Carl paid
= 8 u
= 8 x 8
= $64

Answer(s): $64