SOLUTION: Out of a total of 365 days in a year, Charles runs on 167 days, swims on 138 doays and bikes on 109 days. He swims and bikes on 78 days, swims and runs on 44 days nad bikes and ru

Question 620814: Out of a total of 365 days in a year, Charles runs on 167 days, swims on 138 doays and bikes on 109 days. He swims and bikes on 78 days, swims and runs on 44 days nad bikes and runs on 33 days. If Charles does all three activities on 30 days, on how many days does he do two or more of these events?
The answe is 95 days, but i have no idea how to figure it out.
Thanks in advance
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Out of a total of 365 days in a year, Charles runs on 167 days, swims on 138 doays and bikes on 109 days. He swims and bikes on 78 days, swims and runs on 44 days nad bikes and runs on 33 days. If Charles does all three activities on 30 days, on how many days does he do two or more of these events?
The answe is 95 days, but i have no idea how to figure it out.
Thanks in advance

Before starting this problem, it's recommended that you draw a 3-circle VENN DIAGRAM, so you can see this much, much clearer, especially after you label the diagram, little by little.

Let biking, running, and swimming be B, R, and S, respectively
Since we have to work this problem from the bottom up, we see that:
BRS = 30 days
BR = 33 days
RS = 44 days
BS = 78 days
Also, B = 109 days
S = 138 days
R = 167 days
And finally, all days active = 365 (Not relevant as this is not required to answer the question asked)

Since BRS = 30, and BR = 33, then BR becomes 3 (33 � 30)
Since BRS = 30, and RS = 44, then RS becomes 14 (44 � 30)
Since BRS = 30, and BS = 78, then BS becomes 48 (78 � 30)

BR (biking and running) = 3

RS (running and swimming) = 14

BS (biking and swimming) = 48

BRS (biking, riding, and swimming) = 30

Therefore, the amount of days that 2 or more activities were performed = , or

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