Question

In a family of three, the father weighed 5 times as much as the child, and the mother weighed 3/4 as much as the father. If the three of them weighed a total of 390 pounds, how much did they each weigh?

A. Father: 300 pounds, Mother: 225 pounds, Child: 15 pounds
B. Father: 250 pounds, Mother: 187.5 pounds, Child: 37.5 pounds
C. Father: 200 pounds, Mother: 150 pounds, Child: 40 pounds
D. Father: 150 pounds, Mother: 112.5 pounds, Child: 27.5 pounds

Answer 1

The weight of the child is 40 pounds, the weight of the father is 200 pounds, and the weight of the mother is 150 pounds.

Step-by-step explanation:

Let's assume the weight of the child is x pounds. According to the given information, the father weighs 5 times as much as the child, so the weight of the father is 5x pounds. The mother weighs 3/4 as much as the father, so the weight of the mother is (3/4)*(5x) = (15/4)x pounds.

The total weight of the family is 390 pounds, so we can write the equation:

x + 5x + (15/4)x = 390

Simplifying the equation:

(4x + 20x + 15x)/4 = 390

39x/4 = 390

Multiplying both sides by 4/39 to solve for x:

x = 40

Therefore, the weight of the child is x = 40 pounds. The weight of the father is 5x = 5*40 = 200 pounds. The weight of the mother is (15/4)x = (15/4)*40 = 150 pounds.