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An environmental agency needs to hire a number of new employees so that 85 of the new employees will be able to monitor water pollution, 73 of the new employees will be able to monitor air pollution, and exactly 27 of the new employees will be able to monitor both. (These 27 are included in the 85 and 73 mentioned above.) What is the minimum number of employees that need to be hired?

 Jan 7, 2019
 #1
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Let's start with the 27 employees that will be able to monitor both. We'll have to hire them, so we start with 27 employees. Now, we need to get to a total of 85 employees that can monitor water pollution. We already have 27 that can monitor water pollution, so we need to hire 58 more employees. Next, we need to get to a total of 73 employees that can monitor air pollution. Again, we already have 27 that can do that, so we need to hire 46 new employees. In total, we need 27+58+46 new employees. I'll let you do that addition. Good luck!

 Jan 7, 2019
 #2
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Venn Diagram solution:

 

 Jan 7, 2019

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