Write a ratio for the question below.

Question

Karl bought x bags of red marbles for y dollars per bag, and z bags of blue marbles for 3y dollars per bag.  If he bought twice as many bags of blue marbles as red marbles, then in terms of y, what was the average cost, in dollars, per bag of marbles?

Answer 1

Total cost of red marbles = xy
Total cost of blue marbles = z.3y = 3 zy
But you know that

Karl bought twice as many bags of blue marbles as red marbles

z = 2x

Therefore, total cost of blue marbles = 3*2x*y = 6xy

 

The formula to calculate the average cost of marbles = Total cost/total bags of marbles

Total cost = xy + 6xy = 7xy

Total bags of marbles = x +z = x +2x = 3x

 

Therefore the average cost = 7xy/3x

Since x is common in both the numerator and the denominator, it cancels out

 

The average cost is = 7y/3