SOLUTION: Ballpoint pens cost $1.50 a dozen for the first two hundred dozen a store buys from a wholesaler $1.25 a dozen for those bought in addition to the first two hundred dozens. If the

Question 1159711: Ballpoint pens cost $1.50 a dozen for the first two hundred dozen a store buys from a wholesaler $1.25 a dozen for those bought in addition to the first two hundred dozens. If the stores buy 250 dozen pens from the wholesaler, what is the average cost of ballpoint pens per dozen?
Found 2 solutions by mananth, greenestamps:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

Ballpoint pens cost $1.50 a dozen for the first two hundred dozen a store buys from a wholesaler $1.25 a dozen for those bought in addition to the first two hundred dozens. If the stores buy 250 dozen pens from the wholesaler, what is the average cost of ballpoint pens per dozen?
cost of first 200 dozens = 1.5 *200 =300
cost of next 50 dozens = 1.25 *50 = 62.50
Total cost = 300+62.50 = 412.50
Average cost of dozen = 412.50/250

= $1.65 /dozen
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The answer from the other tutor contains a simple arithmetic error which leads to a nonsensical answer -- the average cost per dozen can't be $1.65 if the prices per dozen are $1.50 and $1.25.

You can solve the problem with formal algebra the way that tutor tried.

Or you can use this informal method, which (if you understand it) will get you to the answer much faster and with much less work.

The store bought 200 dozen pens at $1.50 per dozen and an additional 50 dozen at $1.25 per dozen. So 200/250 = 4/5 of the pens were bought at the higher price.

That means the average cost per dozen is 4/5 of the way from the lower price to the higher price.

The difference between the two prices per dozen is 25 cents; 4/5 of that is 20 cents. So the average cost per dozen is $1.25+$0.20 = $1.45.

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