Liam, Carl, Valen and Howard paid a total of $294 for a souvenir. Howard paid ⁵₉ of what the rest paid. Liam paid 20% of what the rest paid. Carl and Valen paid an equal amount of money. How much did Valen pay?

Liam	Carl	Valen	Howard	Total
9x3			5x3	14x3
1x7	5x7			6x7
	1	1
7 u	10 u	10 u	15 u	42 u

20%= ²⁰₁₀₀= ¹₅
Liam's share : Total share = 1 : 5

The total amount paid for the souvenir is repeated.  Make the total amount the same.  LCM of 14 and 6 is 42.

Amount that Carl, Valen and Howard paid = 35 u

Amount that Carl and Valen paid
= 35 u - 15 u
= 20 u

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

Amount that Carl and Valen each paid
= 20 u ÷ 2
= 10 u

Cost of the souvenir = 42 u

42 u = 294

1 u = 294 ÷ 42 = 7

Amount that Valen paid
= 10 u
= 10 x 7
= $70

Answer(s): $70