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# Help with Inclusion and Exclusion

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1) A rope is 120 feet long. Starting from one end, make a red mark every 3 feet, make a blue mark every 4 feet, and cut the rope at every mark. (Where there’s both a red mark and a blue mark, we only make one cut, not two.) How many pieces of rope do we have now?

2) A school offers both Spanish and Chinese language classes. This past week,10  students dropped from the Chinese classes, which increased the number of students who take neither class from 27 to 31. How did this change impact the number of students who take the Spanish class but not the Chinese class?
Enter positive numbers to indicate an increase and negative numbers to indicate a decrease.

3) How many positive integers divide evenly into either 144 or 196 but not both?

Thank You!

May 11, 2019

#1
+111455
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1) A rope is 120 feet long. Starting from one end, make a red mark every 3 feet, make a blue mark every 4 feet, and cut the rope at every mark. (Where there’s both a red mark and a blue mark, we only make one cut, not two.) How many pieces of rope do we have now?

To see the answer....note that....in the first 12 feet  we make cut at the  3, 4, 6, 8, 9 and 12 foot marks

So...every 12 feet....we have 6 pieces of rope

So....we have   (10) (6)  =  60 pieces in total

May 11, 2019
edited by CPhill  May 11, 2019
edited by CPhill  May 11, 2019
#2
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9 pieces was wrong

May 11, 2019