Final Review: Of 100 stadium workers, 42 work in concession stands, 88 wear name tags

ak752

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This question confuses the heck out of me and I am in need of help.
Q: [FONT=&quot]Of 100 workers in a stadium, 42 work in the concession stands and 88 are wearing name tags. Of the workers in the concession stand, five-sixths are wearing name tags. Which is the probability that one of the workers is in concessions or is wearing a name tag?[/FONT]
 
This question confuses the heck out of me and I am in need of help.
Q: Of 100 workers in a stadium, 42 work in the concession stands and 88 are wearing name tags. Of the workers in the concession stand, five-sixths are wearing name tags. Which is the probability that one of the workers is in concessions or is wearing a name tag?


Perhaps just draw a box / grid.

1) Label the columns Concession / Other / Total
2) Label the rows Name Tags / Other / Total
3) Supply all the cross-hatching to separate the 9 areas.

Start filling in the boxes! For example, Total-Total is 100.
 
This question confuses the heck out of me and I am in need of help.
Q: Of 100 workers in a stadium, 42 work in the concession stands and 88 are wearing name tags. Of the workers in the concession stand, five-sixths are wearing name tags. Which is the probability that one of the workers is in concessions or is wearing a name tag?
What have you tried? Where are you stuck. It is hard to help when we do not know where you are stuck. Exactly how many of the concession workers wear name tags? Please answer that and try to move on from there. If you can't then ask for assistance.
 
This question confuses the heck out of me and I am in need of help.
Q: [FONT=&quot]Of 100 workers in a stadium, 42 work in the concession stands and 88 are wearing name tags. Of the workers in the concession stand, five-sixths are wearing name tags.

So 5/6(42)= 35 workers in the concession stand are wearing name tags. 88- 35= 53 workers, not in the concession stand, are also wearing name tags.

Which is the probability that one of the workers is in concessions or is wearing a name tag?[/FONT]
There are 42 people working in concessions and 53 workers, not in concessions, wearing name tags. There are 42+ 53= 95 workers "in concessions or wearing a name tag".
 
Because Halls already gave you an answer, I shall show you how to solve this using basic algebra.

\(\displaystyle a = \text {number in concession with name tags.}\)

\(\displaystyle b = \text {number in concession without name tags.}\)

\(\displaystyle c = \text {number not in concession with name tags.}\)

\(\displaystyle d = \text {number not in concession without name tags.}\)

And we have 4 equations.

\(\displaystyle \text {Eq. 1: } a + b = 42.\)equations.

\(\displaystyle \text {Eq. 2: } a = \dfrac{5}{6} * (a + b).\)

\(\displaystyle \text {Eq. 3: } a + c = 88.\)

\(\displaystyle \text {Eq. 4: } a + b + c + d = 100.\)

From equation 1 we get \(\displaystyle b = 42 - a.\)

From equation 3 we get \(\displaystyle c = 88 - a.\)

From equation 4, we get

\(\displaystyle d = 100 - a - b - c = 100 - a - 42 + a - 88 + a = a - 30.\)

From equation 2, we get

\(\displaystyle a = \dfrac{5}{6} * (a + b) = \dfrac{5}{6} * (a + 42 - a) = \dfrac{5 * 42}{6} = 35 \implies\)

\(\displaystyle b = 42 - 35 = 7,\ c = 88 - 35 = 53, \text { and } d = 35 - 30 = 5.\)

Now what do they want to know? They want to know

\(\displaystyle a + b + c = 35 + 7 + 53 = 95.\)

What you learned in first year algebra will see you home, but tkhunny's method may be more intuitive.
 
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