# An art teacher finds that colored paper can be bought in three different packages.  The first package has 20 sheets of white paper, 15 sheets of blue paper and 1 sheet of red paper.  The second...

An art teacher finds that colored paper can be bought in three different packages.  The first package has 20 sheets of white paper, 15 sheets of blue paper and 1 sheet of red paper.  The second package has 3 sheets of blue paper, and 1 sheet of red paper.  The third package has 2 sheets of red paper.  The teacher needs a total of 200 sheets of white paper, 180 sheets of blue paper and 22 sheets of red paper.  How many of each type of package should he order so that he does not have any paper left over?

durbanville | High School Teacher | (Level 2) Educator Emeritus

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First establish a pattern for the ordering:

Package 1 = 20white +15blue + 1 red

Package 2 = ............+ 3 blue + 1 red

Package 3 = .........................+2 red

As the white paper is only avalable in the first package we must  buy 10 (1st package)= 200

We now have  200w + 150 bl + 10 r

(which is 10 times each quantity 20 x 10=200; 15 x 10=150  and 1 x 10=10)'

Similarly with the second package- we can only buy blue from this package now, remembering that we already have 150 sheets of blue and 10 red

Therefore we still need 30 sheets of blue and 12 of red

We must buy 10 of the second package:

3x10=30 blue and 1x10=10 red

Now we have 200 wh + 180 bl + 20 r

We now only need 2 sheets of red and as there are 2 sheets per 3rd package we must buy 1 of the 3rd package

`therefore` We need 10 - 1st package; 10 - 2nd package and 1 - 3rd package