Math word problem

Question

Kim plans to provide a bowl of M&Ms at her party. She wants to mix custom printed M&Ms costing 60c per ounce with bulk M&Ms costing 25c per ounce to create 20lb of a mixture costing 32c per ounce. how much of each type of M&M should she use? 

Answer 1

First, let's state how the units will work with this problem:
(cost per ounce)(number of ounces) = (cost for that item)

Now, let:
     x = number of ounces of custom M&M's
     y = number of ounces of bulk M&M's

So, the cost of combined M&M's is:
         60x + 25y
To check so far,
      If x=10 and y=0, then 10 ounces of only custom M&M's costs $6.00
      If x=0 and y=5, then 5 ounces of only bulk M&M's $1.25

The desired mixture totals 20lb (320 ounces), so x+y=320, or y=320-x.
The desired total cost is (32 cents per ounce)( (x+y) ounces)        [see above]

 

         Custom + Bulk = Combined
            60x   +  25y = 32(x+y)       [in cents]

 

60x + 25y = 32(x+y)
60x + 25(320-x) = 32(320)        [y=320-x, and x+y=320]
60x + 8000 - 25x = 10240
35x = 2240

     x = 64     [64 ounces of custom printed M&M's]

     y = 320-64 = 256       [256 ounces of bulk M&M's]

Check:

  60x = 60(64) = 3840 cents for custom M&M's

  25(y) = 25(256) = 6400 cents for bulk M&M's

           Total cost = 10240 cents = $98.80

         Total weight = x+y = 64 oz + 256 oz = 320 oz = 20 lb [note: 16 oz per lb]

       Cost of mix per ounce = 10240/320 = 32 cents per ounce