Mmmmmmm......Chocolate!
The Vaughan Rangers hockey team is selling chocolate bars as a fundraiser. Only one type of chocolate bar is being sold, and each bar sells for $2.70. Amanda, Ben, Cole and David pool their money together to buy a total of 5 chocolate bars. Amanda paid $8.10, Ben paid $2.70 and Cole paid $1.80. David paid the remainder. They divide the chocolate bars so that the fraction of the total that each person paid is equal to the fraction of the total of chocolate that each person receives.
How much chocolate should each person receive?
(This is your first particularly "challenging" question. Go for it!)
The amount of chocolate that each person is going to get is:
ReplyDeleteAmanda: 3 chocolate bars
Ben: 1 chocolate bar
Cole: 7/10 of a chocolate bar
David: 3/10 of a chocolate bar
The first thing that I had to do was find the amount of money that David would have to pay. To find this, I multiplied the cost of one chocolate bar ($2.70) by 5, since they bought 5 chocolate bars in total (the total of five bars is $13.50). Then I added up the how much Amanda, Ben and Cole paid ($12.60) and subtracted it from the total cost, and I got $0.90 for David's share.
So then I found the percentage of the total that each person has to pay. I found the percentage by dividing the cost each person is paying by the total amount.
Amanda - 8.10/13.5 = 60%
Ben - 2.70/13.50 = 20%
Cole - 1.80/13.50 = 13.3%
David - 0.9/13.50 = 6.7%
Based on the condition that the fraction of the total that each person paid is equal to the fraction of the total of chocolate that each person receives, I then used the percentage to find their share of the chocolate.
Amanda - 60% (of 5) = 0.6 x 5 = 3 chocolate bars
Ben - 20% (of 5) = 0.2 x 5 = 1 chocolate bar
Cole - 13.3% (of 5) = 0.133 x 5 = 0.7 or 7/10 of a chocolate bar
David - 6.7 (of 5) = 0.067 x 5 = 0.3 or 3/10 of a chocolate bar
- Rachel
btw, I may disagree with your response re: Cole & David's share..
Deleteyou could have done 2.70-Coles 1.70=90 cents that David needs to pay
Deletehi Rachel
ReplyDeletethank you for your contribution. The part about how your figured out David's share is well explained.
As for the second part; what have you noticed when converting decimal to percent, then to fraction? Can you figure out the solution to this question without converting the figures twice? Is there another way to solve this problem without figuring out the percentage? or is this the only way?
Hello.
DeleteYes, you can figure out the solution to this question without converting the figures twice. Instead of finding the percentage, you could just get the decimal then go straight to multiplying it by 5 (the total amount of chocolate bars).
Ex.
Amanda - 8.10/13.5 = 0.6 x 5 = 3 chocolate bars
Ben - 2.70/13.50 = 0.2 x 5 = 1 chocolate bar
Cole - 1.80/13.50 = 0.133 x 5 = 0.7 or 7/10 of 1 chocolate bar
David - 0.9/13.50 = 0.067 x 5 = 0.3 or 3/10 of 1 chocolate bar
Total Number of Chocolate: 3+ 1+ 7/10 + 3/10 = 5 chocolate bars
- Rachel
Hellooo.
ReplyDeleteI think that the amount of chocolate that each person receives is:
Amanda: 3
Ben: 1
Cole: 0.7
David: 0.3
Since they question indicated that David paid for the remainder, I added everyone's pooled money ($12.60) and subtracted it from the total ($2.70 x 5 chocolate bars). 13.50 - 12.60 = 0.9.
Then I divided their payments by the unit rate per chocolate bar ($2.70 / bar). I did this because I wanted to find out how much chocolate they get based on how much they paid. When I did this, Amanda and Ben were whole numbers, but Cole and David were decimals. I rounded their values to the nearest tenth. To double check my answer, I added all of their numbers together to see if it equals to $2.70 x 5 (Total money required), and it did. I know that this is correct because the amount of chocolate someone receives through what they paid displays an equivalent relationship of "Paying to Getting", which in turn also answers the question.
Thank you for your response~ =)
DeleteTHE FINAL ANSWER:
ReplyDeleteA [amanda] - 3 chocolate bars
B [ben] - 1 chocolate bar
C [Cole] - 7/10 of a chocolate bar
D [david] - 3/10 of a chocolate bar
PROCESS:
First I have to find how much it will cost for the 5 chocolate bars altogether.To find that I multiplied 1 chocolate bar's cost ($2.70) by the amount of chocolate bars that are being bought (5),
$2.70 (1) X 5 (amount of chocolate bars) = $13.50 (how much 5 chocolate bars cost ALTOGETHER)
Then to continue on with my process I have to find out the share of each person (amanda, ben, cole and david). Since the share of A,B and C are given, I have to find D's share. To find Davids share I will add A,B and C's share, then subtract that from the total cost of 5 chocolate bars ($13.50).
A - $8.10 Now that I have found the total share of A,B and C's I have to find the share of D's by
+B - $2.70 subtracting A, B and C's total share by the actual price for 5 chocolate bars because
+C - $1.80 it will tell me the amount LEFT OVER, which will be D's share in the total cost.
__________
$12.60 $13.50 (5 Chocolate bars) - $12.50 = $0.90 - This is the amount left for David to pay
CONVERSION - FRACTION TO DECIMALS
In order to find the amount of chocolate bar each person gets for the amount they paid I now have to divide the amount each person has to pay by the total amount. The strategy I have used here is conversion , I converted fraction into decimal. I don't need to convert the decimal into a percentage because for the next step I wont be needing/using percentages in my process.
A - $8.10 / $13.50 = 0.6
B - $2.70 / $13.50 = 0.2
C - $1.80 / $13.50 = 0.13
D - $0.90 / $13.50 = 0.06
Now that I have found the decimals for A,B,C and D I have to multiply the decimal by 5 because I am trying to find how much each person gets OF the 5 chocolate bars, "OF" tells me I have to multiply to get my answer I am looking for.
A - 0.6 X 5 = 3 chocolate bars
B - 0.2 X 5 = 1 chocolate bar
C - 0.13 X 5 = 0.65 - (when rounded up) 0.7 - 7/10 of a chocolate bar
D - 0.06 X 5 = 0.3 - 3/10 of a chocolate bar
Thank you for reading bye!
-Kajana
Thank you for your input!
DeleteYou're welcome!
DeleteHow i would do it would be by first figuring out the amount David paid. I would first subtract 1 chocolate bar from the 5 because Ben paid the exact price for 1. Then i did the amount of what Amanda paid and divided that by the price of chocolate bars and got 3 so i subtract 3 from the 4. Now there is one chocolate bar left. It is worth 2.70 and Cole paid $1.80. I did 1.80 divided by 2.70 and it equals 0.666 which is 66% of the last chocolate bar. So that means Ben had the rest which was 34%.
ReplyDeleteBye
thank you for your input~ Can you clarify your final step: what does it mean that Ben had the rest (34%)? What is the dollar value of 34%?
Delete$8.10 divided by $2.70= 3. This means that Amanda should get 3 chocolate bars since she paid $8.10. Ben paid $2.70: the exact price of a chocolate bar, so he gets one. Cole paid $1.80 and that is two thirds of the price of a full chocolate bar. David paid the remainder which was one third of the full price. This means that Cole should get two thirds of the chocolate bar that they paid for together. The other third goes to David since he paid the remainder.
ReplyDeleteThank you for your response; what is the dollar amount David needs to pay at the check out?
DeleteThis is an answer by Jatin and John
ReplyDeleteOur final answer was ben gets 1 chocolate bar, amanda gets 3 chocolate bars, cole gets 2/3 of one bar and david gets 1/3 of a chocolate bar.
We got this answer by first we multiplied the total amount of chocolate bars by the price of 1 chocolate bar. Which was $13.5 in total. Then we added Amanda's, Ben's and Cole's contribution. In total was $12.60. Then we subtracted the total amount of money the friends paid to the total cost of bars. the answer was $0.9. this means that David paid this much money for his share.
We already know that Ben gets one because he paid $2:70 for 1.
We multiply 2.70 by 3 for Amanda.
And we knew that 0.9 is 1/3 of the bar for david
And that means, Cole paid 2/3 of a bar
That is our 2 cents
so do you guys get a bite of the bar for your 2 cents? =)
Deletethank you for your input; can you clarify your final two lines: "and We knew..." how do you know? Why is 0.9 1/3 of the bar?
First, I had to find out how much David paid. So, because 1 bar equals 2.70 dollars, I multiplied it by 5. I got $13.50. Now I know that altogether they must have paid 13.50. So, I added Amanda, Ben and Cloe’s money and got 12.60. The rest must have been how much David paid. I subtracted 13.50 from 12.60 and got 90 cents. Therefore, I now know that David paid 90 cents.
ReplyDeleteNow, I need to find out how many candy bars Amanda’s amount, $8.10, can get her. I used trial and error to find out how many candy bars she could buy for $8.10. I ended up with 3. Therefore, Amanda should get 3/5 bars. Now, I need to find out how many candy bars Ben’s amount, $2.70, can get him. I used trial and error to find out how many candy bars she could buy for $2.70. I ended up with 1. Therefore, Ben should get 1/5 bars. Now, I need to find out how many candy bars Cole’s amount, $1.80, can get her. I used trial and error to find out how many candy bars he could buy for $1.80. I ended up with 0.7. Finally, I need to find out how many candy bars David’s amount, $0.90, can get him. I used trial and error to find out how many candy bars he could buy for $0.90. I ended up with 0.3.
Another great session of POTW. Keep up the awesome work. Your teachers love reading these threads and seeing the various ways students come up with solutions, as well as the rich dialogue between bloggers. Below is another solution provided for the math problem.
ReplyDeleteSolution:
If Amanda, Ben, Cole and David buy a total of 5 chocolate bars at $2:70 per
bar, then they paid a total of 5 $2:70 = $13:50.
Amanda paid $8.10, Ben paid $2.70, Cole paid $1.80 and David paid the
remainder. Therefore, David paid $13:50 - $8:10 - $2:70 - $1:80 = $0:90.
Amanda should receive 8.10/13.50 = 81/135 = 3/5 of the total amount of chocolate.
So Amanda should receive 3/5 of 5, or 3/5 x 5 = 3 chocolate bars.
Ben should receive 2.70/13.50 = 27/135 = 1/5 of the total amount of chocolate.
So Ben should receive 1/5 of 5, or 1/5 x 5 = 1 chocolate bar.
Cole should receive 1.80/13.50 = 18/135 = 2/15 of the total amount of chocolate.
So Cole should receive 2/15 of 5, or 2/15 x 5 = 2/3 of a chocolate bar.
David should receive 0.90/13.50 = 9/135 = 1/15 of the total amount of chocolate.
So David should receive 1/15 of 5, or 1/15 x 5 = 1/3 of a chocolate bar.
We should check that all of the chocolate has been distributed. If there were
any errors in our solution, this may help us catch them. Amanda receives 3
chocolate bars, Ben receives 1 chocolate bar, Cole receives 2/3 of a chocolate bar
and David receives 1/3 of a chocolate bar. The total number of chocolate bars
distributed is 3 + 1 + 2/3 + 1/3 = 5, as required.