Question 640701
let the cost of dinner be x

Mary paid x/3
Julie 1/2 * x/3= x/6

Balance $75 Peter paid

x/3 + x/6 +75 = x

x/3+x/6 -x= -75

LCD = 6

multiply equation by 6
2x+x-6x=-450

-3x=-450
/-3
x=150

Mary paid 1/3 of 150 = $50
Julie paid 1/6 of 150 = $25
Peter paid $75

Add up 
The total cost of dinner = $150