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A teacher uses 2/3 of her yearly supply of construction paper during the first quarter. She then uses 5/7 of what's left during the second quarter. During the third quarter, she uses 3/4 of what she has left (from the end of the second quarter). How much construction paper does the teacher have left for the fourth quarter of the school year?

 Dec 20, 2021
 #1
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A teacher uses 2/3 of her yearly supply of construction paper during the first quarter. She then uses 5/7 of what's left during the second quarter. During the third quarter, she uses 3/4 of what she has left (from the end of the second quarter). How much construction paper does the teacher have left for the fourth quarter of the school year?

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Construction paper => x

 

2x/3 + 5x/21 + 6x/84 = 82x/84

 

Construction paper left = x/42    or    1/42

 Dec 20, 2021
 #2
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Easy Method -

1 - 2/3 = 1/3

1/3 - 1/3 * 5/7 = 1/3 - 5/27 = 2/27

2/27 - 2/27 * 3/4 = 2/27 - 6/84 = 2/7 - 7/14 = 7/42

The teacher has 1/42 of paper left in the fourth quarter of the school year

 Dec 20, 2021

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