Make sure to thoroughly explain how you solved the problem. Show your mathematics and explain as you go so we understand what the numbers are and where you got them or why they are important.

Good luck,

Ms. L.

To begin the problem you had to account for the proportions or ratios of items to solve the problem. Anne used one piece of paper per letter and Sue used three pieces of paper per letter. If you thought about the number of materials per letter you could set up a table of paper and envelopes per letter. Doing so you would want to add 50 to the number of papers Anne used because she had fifty left over, and you would want to add 50 to Sue’s envelopes as she had 50 envelopes left over. Then all you needed to do was test various numbers of letters, and continue until the total paper and total envelopes were the same for both girls.

Here is the table I made. You can see from the table the girls started with 150 pieces of paper and 100 envelopes.

Here is another table done by AH:

## 22 comments:

To solve the question, I needed to sort the information out that I already knew.

Ann

• Used to write 1-sheet letters (Ann wrote 100 letters.)

• Used all the envelopes

• 50 sheets of paper left

Sue

• Used 3-sheet letters (sue wrote 50 letters.)

• Used all sheets of paper

• 50 envelopes left

Then I multiplied 50 by 3 and got 150, then -50 equals 100.If you simplify that, it would equal 3/1, and so that means that for every envelope, there are 3 pieces of paper. Then I stareted thinking about all the ties between all the envelopes and letters for Sue and Ann, because I was confused. I finally sorted out that since Ann wrote 100 letters, and had 50 sheets of papers left, that means there are 150 papers, and 100 envelopes. In conclusion, the stationary came with 100 envelopes and 150 papers.

JW

POW

C.J.H.

Ann writes one sheet letters and has 50 pieces of paper left and no envelopes, and Sue writes three sheet letters and has used all her pieces of paper but has 50 envelopes left.

So if there are 150 sheets, then Sue would have written 50 letters, and if there was 100 envelopes then Sue would have 50 envelopes left. If Ann wrote 100 letters she would use all 100 envelopes and would have 50 sheets of paper left.

The stationaries have 100 envelopes and 150 sheets.

Ann- used all of the envelopes and had 50 sheets of paper left Uses 1 piece of paper.

Sue- used all of the envelopes and had 50 sheets of paper left. Uses 3 pieces of paper

I think that Ann started out with 100 and Sue started out with 150 pieces of paper. The ratio would be 3/1 for Sue because she used 3 pieces of paper per letter. Sense they had the same stationary set they both had 100 envelopes each. Then it took sue to write 50 letters because Sue wrote 3 pieces of paper per letter and you divide 150 by 3 and equals 50. In that case she wouldn’t have anymore pieces of paper left and wrote 50 letters in total. Ann wrote 100 letters because she only used 1 piece of paper per letter and started out with 100 envelopes and paper.

sm

POW NH

A: Ann writes 1 sheet letters ______ Sue writes 3 sheet letters

Ann 50 left sheets

Sue 50 envelopes left

They used all they’re envelopes

so they had 100 envelopes

and 150 sheets of paper.

Since Sue used all her pieces of paper, that means that 50 * 3 sheet letters = 150 sheets of paper. And since there’s 150 sheets of paper, and Ann had 50 sheets of paper left 150- 100 = 50 sheets left. So, if Ann wrote 100 letters than that means there is 100 envelopes

Ann- one sheet letters (Ann used all the envelops) Had 50 pieces of paper left

Sue- three sheet letters (Sue used all the sheets of paper) had 50 envelopes left

I think that they started out with 150 pieces of paper.

Then I think that they started out with 100 envelopes

Sue used 150 pieces of paper.

The ratio would be 3/1 for sue because she used 3 pieces of paper per letter.

If you divide 150 by 3 you get 50.

So sue used 50 envelopes, and had 50 envelopes left.

(50+50= 100)

Ann used 100 pieces of paper.

Her ratio would be 1/1 because for every piece of paper she used one envelope.

If you subtract 100 from 150 you get 50

(150-100=50)

So she had 50 pieces of paper left.

Ann used 100 envelopes and had no envelopes left

!!HR!!

How many sheets of paper did Ann and Sue start out with?????

In the problem, I was given some information about number of letters and envelopes and was asked to figure out how many papers the girls started out with. I think that the girls started out with 150 sheets of paper because the ratio would be 3/1. That would be the ratio because the way to set it up would be Sue/Ann. Since there are 150 pieces of paper, and Ann had used all of the envelopes but had 50 papers left over then she would have 100 envelopes to begin with. I know that Sue had 100 envelopes because she used 3 sheets of paper per letter and had 50 envelopes left over so I did 150/3=50 and then 150-50=100 and so 100 is the number of envelopes and 150 is the number of sheets of paper.

SV

Anne used 1 sheet for her letters

Sue used 3 sheets for her letters

Anne had 50 pieces of paper left

Sue had 50 envelopes left

Question- How many sheets of paper in the box to begin with?

How many envelopes were in the box to begin with?

Paper- 150 to begin with 50*3=150

Ratio: 3/1

Envelope- 100 envelopes

150/3=50

150-50=100

To begin with there were 150 pieces of paper and 100 envelopes

Anne used one sheet of paper for her letters. Sue used 3 sheets of paper for her letters. Anne ended up using all of the envelopes, but had 50 pieces of paper left. Sue ended up using all of the paper, but had 50 envelopes left. The question is how many envelopes and how much paper were in the box to begin with. Well, if you mulitiply 50 time 3 you get 150, so that is how much paper was in the box to begin with. The ratio of that is 3/1. Then if you do 150/3 you get 50, if you subtract 50 from 150 you get 100, and that tells us how many envelopes were in the box in the beginning.

JL1

R.B. POW

Ann and Sue bought boxes of stationery with 75 sheets and 75 envelopes. For Ann, you do 75 sheets minus 50 sheets (she had 50 sheets left) leaves you with 25 letters and 25 envelopes. For Sue, you would do 75 envelopes minus 50 (she has 50 envelopes left) is 25 envelopes and 75 sheets divided by 3 is 25 so she has 25 envelopes and 25 letters.

Anne-used 1sheet per letter, 50 papers left over

Sue- used 3 sheets per letter, 50 envelopes left over

Question: how many sheets of paper and envelopes did they start out with.

3x50= 150 because Sue used 3 sheets of paper per letter and used all the paper.

They started out with 150 papers

Ratio: 3/1

150/3=50

150-50=100

They started out with 100 envelopes.

Sue and Ann started out with 150 papers and 100 envelopes. I know this because Sue used 3 papers per letter and used all the paper. So 3 times 50 equals 150. I know that there are 100 envelopes because 150 divided by 3 equals 50 and 150, which is the number of envelopes, minus 50 is 100 which tells us that there were 100 envelopes in the box to begin with.

EK

Ann used 3 pieces of paper to write one letter while Sue used 1 piece of paper to write 1 letter. Ann has 50 pieces of paper left and Sue has 50 envelopes left. To figure out the paper I just did 50x3 to get 150. I know this was right because 3 goes into 150 evenly (50 times) and Sue must have written 100 letters because 150-100= 50, and she had 50 pieces of paper left. So in conclusion there was 150 pieces of paper.

For the envelopes I figured there were 100. I figured this out because Sue wrote 150 letters and 150/3= 50 letters. 100-50=50, that’s 50 letters left. Then for Sue she wrote 100 letters so then she used all the 100 envelopes and that’s how many the stationary gave them.

JL2

M.R

Ann.) 150-100 =50

100-100=0

Sue.) 150-150=0

100-50=50

Ann used x sheets to have 50 sheets left so lets say he use 150 sheets and 100 envelopes so 150-100= 50 now for sue she uses 3x sheets so 150 sheets after 50 envelopes we have 150/3=50-50 is 0 meaning 50 envelopes have been used up so we have 50 envelopes left so basically…

Ann used all her envelopes she had 100 of them she had 150 sheets of paper that make 1 sheet uses one envelope so she has 50 sheets left. Now that that part is out of the way think of 3 used for every envelope you would use 50 envelopes because 150-(50*3) is 0 and the 50 stands for how many envelopes you send and 100-50 is 50 envelopes.

The answer to the problem is 150 sheets of paper and 100 envelopes.

E.K. POW

There were 150 sheets of paper and 100 envelopes. See, Anna writes 1 sheet of paper per letter and has 50 sheets left. Meaning that she wrote 100 letters, because there are 100 envelopes, 150-100=50 the amount of paper left. Sue writes 3 sheet of paper pre letter and has 50 envelopes left. 3 goes into 150, 50 times, using all the paper, and 50 is the number of envelopes used for all the letters which is half the amount of envelopes leaving 50.

I multiplied 3 by 50 to get 150 papers for Sue. Since she used all the papers but put 3 papers in each envelope, I divided 150 by 3 to see how many envelopes she would need and got 50. Since I know she has 50 envelopes left, I added 50 to 50 and got 100. Now that I had an idea of what the answer might be, I checked my answer with Ann.

I know that ann doesn’t have any envelopes left but has 50 papers left and that she only puts one paper per envelope. So I took 150 and subtracted 50 and got 100, so I know she used 100 papers. Then I know she put one letter in each envelope so if she has 100 envelopes and she uses 100, she doesn’t have any left. Then I knew my answer was right.

Final Answer= they each had 150 papers in total and 100 envelopes.

By : AH

J.B. POW

They had 150 sheets of paper and 100 envelopes. Ann wrote 1 sheet of paper for every letter she writes and has fifty left so I thought that she must’ve used one hundred sheets then I did Sues 50 envelopes left and I was sure that they had 150 sheets of paper. Sue wrote three sheets of paper every letter and she used 50 envelopes so I did 50x3 equals 150 sheets of paper, I also got Ann’s 50 sheets of paper by doing this.

Solving of the problem!!!

Sue: 3x50=150 in all but there are 75 papers and 75 envelopes in the package

Ann: 1x50=50+50=100 in all 50 envelopes but also 75 papers and 75 envelopes in the package

Explaining my solving powers!!!

I found out that Sue used 3 pieces of papers for each envelope. So what I did was 50 times 30 equals 150. I know that was the total of all the papers and envelopes, so I divided that by 2 to get the amount of papers and envelopes, which were 75 for each.

Ann was pretty easy, I multiplied 1 by 50 because she used one sheet per envelope plus 50 more sheets she used which made 100 papers. 150 minus 100 gets you 50 envelopes are left.

-B.B.!!!

J. K. the Blondie 11/9/07

Ann and Sue bought identical boxes of stationery. Ann used hers to write one sheet letters, and Sue used hers to write three sheet letters. Ann used all the envelopes and had 50 sheets of paper left, while Sue used all of the sheets of paper and had 50 envelopes left. How many sheets of paper and how many envelopes were in the box to begin with?

There are 150 pieces of paper and 100 envelopes in each box of stationary. I used guess and check. First, I looked to see if the conclusion I made was possible for Ann. Ann uses 1 paper to write letters so she uses 1 envelope per piece of paper. If Ann used all envelopes and had 50 sheets of paper left, the box would have to have 100 envelopes and 100 papers, (1 envelope per paper) but she had 50 pieces of paper left over, so the box contains 150 pieces of paper and 100 envelopes. Then I tried to see if my conclusion was also correct for Sue because they bought the same identical box of stationary. Sue uses 3 pieces of paper for her letters and every letter equals one envelope. So, for Sue, 3 pieces of paper every envelope. Sue had 50 envelopes left so she used 50 envelopes (100 total envelopes minus 50 left over) for 150 pieces of paper, if my conclusion is correct for Sue. 3 pieces of paper every envelope for Sue. 150 papers divided by 3 papers each envelope, equals 50 envelopes, plus 50 leftover envelopes, equals 100 envelopes, 150 pieces of paper.

O. S.

11/9/07

P. O. W.

Both stationary packages have 150 pieces of paper and 100 pieces of envelopes. I had first gotten my answer by doing 50 envelopes and 100 papers. Since Ann uses 1 piece of paper for 1 letter, you have to subtract the same on both sides. I subtracted 50 from 50 and got 0 envelopes. I subtracted 50 from 100 and got 50 papers. Ann would have 50 papers left and used all of her envelopes. I tried figuring out if 50 envelopes and 100 papers would also work with Sue because they need to have identical boxes, but it turns out that she needs more papers and envelopes. I then used 150 papers and 100 envelopes and it had worked for both of them.

Ann and Sue- 100 envelopes 150 papers

Ann:

150 papers 150-100=50 papers

100 envelopes 100-100=0 envelopes

Sue:

150 papers 150-150=0 papers

100 envelopes 100-50=50 envelopes

Ann has used all her envelopes and has 50 sheets of paper left.

Sue has used 50 of her envelopes and has used all her papers.

If Ann used to write one sheet letters, she must have used 100 sheets of paper to have 50 left, because Sue used three sheet letters, and she had 50 envelopes left, so she must have used 50 envelopes to do 50x3+150. Then for Ann if she used 100 sheets of paper and had 50 left, it would be 150-100. It all fits in as a puzzle. So the boxes of stationery contain 150 sheets of paper and 100 envelopes.

D.E.

POW M.R.G.

Ann one sheet letters 50 papers left she used all the envelopes

Sue writes three sheets letters 50 envelopes she used all the sheets of paper

They have 100 envelopes and 150 pieces of papers. The reason I know that is by Sue wrote three sheet letters and Ann had 50 left so 3 multiplied by 50 is 150 pieces of papers. The reason I know its 100 envelopes is by Ann having 150 sheets of paper and had 50 left so 150 minus 50 is 100. Ann also used all her envelopes so the amount of envelopes is 100. That is how I got my answer of 100 envelopes and 150 pieces of paper for each stationary.

S.S P.O.W 11/9/07

There are one hundred fifty pieces of paper and one hundred envelopes in each stationary box. I guessed different numbers until one of them would fit. For Sue I did one hundred fifty pieces of paper divided by three it was fifty, leaving Sue with zero pieces of paper and fifty envelopes. So the box would have to have one hundred fifty pieces of paper and one hundred envelopes and they also have to be the same For Ann. Ann used one piece of paper for each letter so she used all of the envelopes and had fifty pieces of paper remaining. So in conclusion each stationary box contains one hundred envelopes and one hundred fifty pieces of paper.

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