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

Hi Joyce,

 

Let's begin by stating the given cost per marble bag for each colored marble:

    cost of red marble bag = y / x

    cost of blue marble bag = 3y / z

 

Since we are told that Karl bought twice as many blue marble bags than red marble bags, we can replace z (blue marble bags) with 2x (twice the number of red marble bags) in our 2nd cost expression above:

    cost of blue marble bag = 3y / z

    cost of blue marble bag = 3y / 2x

 

Our average cost of per marble bag will be:

(cost per red marble bag + cost per blue marble) / 2:

    ((y / x) + (3y / 2x)) / 2 = ( (y + 3y) / (x + 2x) ) / 2

                                = (4y / 3x) / 2

                                = (4y / 3x)(1 / 2)

                                = (4y times 1) / (3x times 2)

                                = 4y / 6x

                                = (2(2y)) / (2(3x))

                                = 2y / 3x

 

average cost per marble bag = 2y / 3x

 

The key to solving problem was realizing that we could express the number of bags of one colored marble in terms of the number of bags of the other colored marble.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.