Rick gave 1/4 of his money and an additional $1 to Maria. He gave 1/5 of his remaining money and an additional $4 to Sophia. The amount of money Rick had left in the end was $31 more than the amount of money he gave to Sophia. Find the amount of money Rick gave to Maria
Let the amount of money Rick have = x
Then amount of money given to Maria = x/4 + 1
Amount of money given to Sophie = 1/5 (x(x/4 + 1)) + 4
Amount left at the end = 3 + 1/5 (x - (x/4 + 1)) + 4 + 31
x/4 + 1 + 1/5 (x - (x/4 + 1)) + 4 + 1/5 (x - (x/4 + 1)) + 4 + 31 = x
=> x/4 + 1 + 1/4 (3x/4 - 1) + 4 + (3x/4 - 1) 1/5 + 35 = x
X/4 + 1 + 3x/20 - 1/5 + 4 + 3x/20 - 1/5 + 35 = x
=> 40 - 2/5 = x - 6x/20 - x/4
(200 - 2)/5 = (20x - 6x - 5x)/20
198/5 = 9x/20
x = (20 * 198)/5 * 9
=> x = 88
Amount of money given to Maria = 88/4 + 1 = 22 + 1 = $23
