fractions

[anushka]

Tania made some paper cranes. 2/7 of the paper cranes were yellow and 1/5 of the remiander was blue. the remianing paper cranes were orange. if she made 70 more yellow cranes than blue ones, how many orange cranes did she make?

 

[daon2]

Let Y,B,O be the number of yellow, blue and orange cranes respectively. Then the total number of cranes is Y+B+O.

What other relationships have you been given between them?

 

[cmallen]

Yellow = 2/7

1/5 of the remainder (5/7) = blue = 1/7

The remaining paper cranes are Orange = 4/7

Yellow = B+70 ... Thus, 1/7 = 70

Yellow = 140

Blue = 70

Orange = 280

But the answer in the book is 140, I don't get how they get 140? I think it should be 280.

Help. Thanks in advance!

 

[Steven G]

Orange = 280.

 

[HallsofIvy]

Yellow = 2/7

This makes no sense! Surely you don't mean only 2/7 of a paper crane was yellow. You are told that 2/7 of all the paper cranes made were yellow. Start with "Let N be the total number of paper cranes". Then you can say "Yellow= (2/7)N".

1/5 of the remainder (5/7) = blue = 1/7

Better: the remainder is N- (2/7)N=(5/7)N and 1/5 of that is (1/7)N.

The remaining paper cranes are Orange = 4/7

a
Yellow and blue paper cranes account for (2/7)N+ (1/7)N=(3/7)N so the remainder is N- (3/7)N=(4/7)N. There are (4/7)N orange paper cranes, not 4/7 of a paper crane!

Yellow = B+70 ... Thus, 1/7 = 70

Do you really think that "1/7" is equal to "70"?
Yes, because "she made 70 more yellow cranes than blue ones" and you already have that there are (2/7)N yellow cranes and (1/7)N blue cranes, (2/7)N= (1/7)N+ 70 so (2/7)N-(1/7)N= (1/7)N= 70, N= 490. She made a total of 490 paper cranes. There are (2/7)N= (2/7)(490)= 2(70)= 140 yellow paper cranes, (1/7)(490)= 70 blue paper cranes, and 490- 140-70= 490- 210= 280 orange paper cranes.

Check: "2/7 ofthe paper cranes are yellow": (2/7)(490)= 140.
"1/5 of the remainder are blue". The remainder is 490-140=350. 1/5 of that is 70.
"The remaining paper cranes are orange". 490- 140- 70= 490- 210= 280.
"she made 70 more yellow cranes than blue ones". 140- 70= 70. Yes, 140 is 70 more than 70.

Yellow = 140

Blue = 70

Orange = 280

But the answer in the book is 140, I don't get how they get 140? I think it should be 280.

Are you sure you read the problem correctly? If so then the book is wrong. There were 140 yellow paper swans and 280 orange paper swans.

Help. Thanks in advance!

 

[Deleted member 4993]

Orange = 280...............Incorrect. Name of a color cannot equate to a number ... → .... corner time

 

[cmallen]

This makes no sense! Surely you don't mean only 2/7 of a paper crane was yellow. You are told that 2/7 of all the paper cranes made were yellow. Start with "Let N be the total number of paper cranes". Then you can say "Yellow= (2/7)N".


Better: the remainder is N- (2/7)N=(5/7)N and 1/5 of that is (1/7)N.

a
Yellow and blue paper cranes account for (2/7)N+ (1/7)N=(3/7)N so the remainder is N- (3/7)N=(4/7)N. There are (4/7)N orange paper cranes, not 4/7 of a paper crane!


Do you really think that "1/7" is equal to "70"?
Yes, because "she made 70 more yellow cranes than blue ones" and you already have that there are (2/7)N yellow cranes and (1/7)N blue cranes, (2/7)N= (1/7)N+ 70 so (2/7)N-(1/7)N= (1/7)N= 70, N= 490. She made a total of 490 paper cranes. There are (2/7)N= (2/7)(490)= 2(70)= 140 yellow paper cranes, (1/7)(490)= 70 blue paper cranes, and 490- 140-70= 490- 210= 280 orange paper cranes.

Check: "2/7 ofthe paper cranes are yellow": (2/7)(490)= 140.
"1/5 of the remainder are blue". The remainder is 490-140=350. 1/5 of that is 70.
"The remaining paper cranes are orange". 490- 140- 70= 490- 210= 280.
"she made 70 more yellow cranes than blue ones". 140- 70= 70. Yes, 140 is 70 more than 70.

Thanks for the validation. I copied the problem word for word. Agree with you that the book is wrong but wanted another set of eyes to review it. THANKS.