For 4 family members with one that eats the same amount as the other 3 combined how do you calculate each person's fair share of food cost?

Answer 1

Since one person--whom we'll call person four--eats 3 portions of food for each 1 portion consumed by the other 3 persons, consider the total shares of food--and thus cost--to be 6. That is, 1 each for the first 3 persons plus 3 for the fourth. So persons one, two, and three will each pay 1/6 of the cost, and person four--the big eater--pays 3/6, or 1/2, of the cost! ----------------- Algebraically, we would work the problem like this: Let x stand for the cost share of any of the 3 light eaters; let y stand for the cost share of the 1 heavy eater. Let c stand for cost of the groceries. Now you can say x + x + x + y = c, or 3x + y = c. Since we know the heavy eater's share equals that of the other three combined, we can say y = x+x+x, or y = 3x. Solve the equations for x (a light eater's share of the cost): * 3x + y = c * 3x + 3x = c [substituting 3x for y, from the second equation] * 6x = c * x = c/6, or 1/6 of c. So each light eater pays 1/6 of the cost. Now solve the equations for y (the heavy eater's share of the cost): * 3x + y = c * y + y = c [substituting y for 3x, from the second equation] * 2y = c * y = c/2, or 1/2 of c. So the heavy eater pays 1/2 of the cost.