How many extra banners can be made?

Question

Students are making banners for the assembly, pep-rally and bonfire on Friday before the big game.

The school colors and blue and white.

 

Each banner requires 1/4 yard of blue material and 3/8 yard of white material.

 

500 banners are needed as there are no more than 500 students and teachers.

That is, there MUST be at least 500 banners, no less.

 

The blue material is sold in rolls of 10 yards and the white material is sold

in rolls of 12 yards.

 

If enough (whole number) rolls are purchased so as to make 500 banners,

how much material is left over in excess and how many extra banners can be made with the excess?

 

The book says the answer is 12, but I keep getting 16. Can someone please help?

12 does not seem like enough. Can someone prove that the answer is not 12?

I think it is a mistake (mis-print) in the book, but I keep trying......

 

Thank you to all of the awesome and amazing tutors!!! You all are greatly appreciated

for all that you do.

Answer 1

Thank you for your kind words.

Blue:
500 banners x 1/4 yard = 500/4 yd = 250/2 yd= 125 yards

White:
500 banners x 3/8 yard = 1500/8 yd = 750/4 yd = 375/2 yd = 187.5 yards

As each roll of blue is 10 yards, they need 125/10 = 12.5 rolls.
So they must purchase 13 whole rolls of blue.

Likewise each roll of white is 12 yards, so they they need 187.5/12 = 15.625 rolls.
So they must purchase 16 rolls of white.

Altogether, that is 10 x 13 = 130 yards of blue.
So there is 130 - 125 = 5 yards of excess blue material

and 12 x 16 = 192 yards of white material which is
192-187.5 = 4.5 yards extra of the white material.

From this excess material, they have enough blue material to make
5 divided by 1/4 = 5 x 4 = 20 banners and 4.5 divided by 3/8 =
4 and 1/2 divided by 3/8 = 9/2 divided by 3/8 = 9/2 x 8/3 = 72/6 = 12 banners.

Therefore, they can only make 12 whole banners extra.
They will have enough blue material to make 20-12=8 more banners
IF they had more white material, but they don't.

The text book is correct.

Answer 2

125 yards of blue (500 x 1/4), 13 rolls, five yards left over, 20 possible banners

187.5 yard of white (500 x 3/8), 16 rolls, 4.5 yards left over, 12 possible banners

 

Did you use 12 yards per roll for the white?