Gross Profit Word Problem

[vrowland]

A shipment of 1500 heads of cabbage each of which was approximately the same size was purchased for $600. The day the shipment arrived 2/3 heads were sold, each at 25 percent above the cost per head. The following day the rest were sold at the price per head equal to the 10 percent less than the price each head sold for one day before. What was the gross profit on this shipment?

[vrowland]

Can someone please explain this problem to me?

[indiantiger]

Here is how I would approach the problem :

Given :

Total number of product = 1500
total purchase price = 600
purchase price per cabbage head = 600/1500 = 6/15 = 2/5

Gross profit = selling price - purchase price

selling price = cabbage sold on first day + cabbage sold the next day
cabbage sold on first day = 2/3*1500 * {2/5 +2/5*1/4}=1000 *2/5(5/4)
=1000*1/2
= 500

cabbage sold on next day = 1/3*1500 *{2/5-2/5*1/10} = 500 {2/5(9/10)} = 10*18
= 180
total selling price of cabbage = 500+180 = 680

gross profit = 680-600 = 80(whats the OA?)

I hope this helps.

[indiantiger]

slight mistake on my part for the second day sale it should be
= 1/2 - 1/2*1/0 (10% less than the last day's price)
= 1/2*9/10 = 9/20
total sale price for second day = 9/20*500 = 450/2 = 225

total gross profit = 500 + 225 -600 = 725-600 = 125

I hope this time not wrong.

[thephoenix]

$125

total=1500
cost=600
cost per head=600/1500=2/5

25% above--->5/4*(2/5)=1/2
2/3 of heads--->1000
cost=1000*2=500

10% less of one days back price=9/10*1/2=9/20
left quantity=500
cost=500*9/20=225

tot selling price=500+225=725
profit=125

[outreach]

price of each cabbage=600/1500=$0.40

125 percent of each cabbage=$0.50

2/3 of 1500 cabage=1000. 1000 sold at 25 percent above the cost head...total price=1000*0.50=500

10 percent less than the price each head sold for one day before, means each cabbage will be sold for 0.45(0.9*$0.5)
hence total proice of remaining 500 cabbage is =500 * 0.45=225

hence total money earned by selling is $725

Gross profit = $125

A shipment of 1500 heads of cabbage each of which was approximately the same size was purchased for $600. The day the shipment arrived 2/3 heads were sold, each at 25 percent above the cost per head. The following day the rest were sold at the price per head equal to the 10 percent less than the price each head sold for one day before. What was the gross profit on this shipment?

[vrowland]

Thank You! I got it now.