SOLUTION: There are two types of pumpkins, large ones that sell for $9 and small ones that sell for $4. A total of 80 pumpkins were sold that totaled $395. How many of each were sold? I

Question 29586: There are two types of pumpkins, large ones that sell for $9 and small ones that sell for $4. A total of 80 pumpkins were sold that totaled $395. How many of each were sold?
I figured I would begin 9a + 4b = 395, then that would equate to 9a = 395 - 4b. However, I don't know what to do next. Please help.
Thanks. Matt
Answer by sdmmadam@yahoo.com(530) (Show Source): You can put this solution on YOUR website!
There are two types of pumpkins, large ones that sell for $9 and small ones that sell for $4. A total of 80 pumpkins were sold that totaled $395. How many of each were sold?
I figured I would begin 9a + 4b = 395, then that would equate to 9a = 395 - 4b. However, I don't know what to do next. Please help.
Thanks. Matt
Let the number of large pumpkins be L
and let the number of small pumpkins be S
The total number of pumpkins = 80
Therefore L+S = 80 ----(1)
Each large sells at $9 and hence L large pumpkins would sell at LX9 =9L
Each small sells at $4 and hence S small pumpkins would sell at SX4 =4S
The total sale amount is $395
Therefore 9L + 4S = 395 ----(2)
(1) implies L= (80-S) ----(*)
Putting (*) in (2)
9L + 4S = 395 ----(2)
9(80-S) +4S= 395
720-9s+4s= 395
-9s+4s= 395-720 (grouping like terms,changing sign while changing side)
-5s = -325
s= (-325)/(-5)= +65
There are 65 Small pumpkins.
Putting S=65 in (*),
L=(80-S)
L= 80-65 = 15
Therefore there are 15 Large pumpkins
Answer; No of Large pumpkins = 15 and the number of Small pumpkins = 65
Verification : Putting L=15 and S=65 in (2)
LHS = 15X9 + 65X4 = 135+260 = 395 = RHS
Therefore we are correct

Note: You would like to know why the problem could not be handled properly!
I must congratulate you. You have a fine business knack and you have got onto the money part of the pumpkins correct. But what about the total number of pumpkins? That is the oversight! Such oversights have happened to great souls like Newton and Archemedes. Don't you worry. The therory part of math which is boring to the students at the level they are bombarded with it is very handy when you are not able to visualise things and when everything is a hzy blaze.
Let me point out things about this problem correlated with your thought process!
By the way what is your a and what is your b?
While answering you must always hit the nail on the head.
But congratulations! your intuition is right and the equation is right. What is running through your mind is that a is the total number of large pumpkins and b is the total number of small pumpkins.
Each large sells at $9 and hence 'a' large pumpkins would sell at aX9 =9a
Each small sells at $4 and hence 'b' small pumpkins would sell at bX4 =4b
The total sale amount is $395
Therefore 9a + 4b = 395.
Very correct and very good.
But in your hurry to get the total number of large and total number of small ones and be done with the problem, a simple fact that since there are two variables a and b there should be two equations and so we have to look for another equation in terms of a and b is lost sight of -you got it!
Let me give you a real life example.
If the family has decided to go the mall where fabulous sale has been announced, in our hurry in getting to the mall,if we forget to take with us the important people in the vehicle, (the people responsible for going to the mall or say the people who are important for the purchase,)what would be the situation?
We are given that a total of 80 pumpkins were sold
So the most vital information is (a+b) = 80
That is it.
I have literally talked to you like your class teacher doing the post mortem after getting your paper back.
Thank you very much for the patient reading!
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