Sapphire Island is open 7 days a week. The park has 8 ticket booths, and each booth has a ticket seller from 10:00 a.m. to 5 p.m. On average, ticket sellers work 30 hours per week.

Write and solve an equation that can be used to find t, the minimum number of sellers the park needs. Interpret the solution.

The park plans to hire 20% more than the minimum number of ticket sellers needed in order to account for sickness, vacation, and lunch breaks. How many ticket sellers should the park hire?

Question

06-09-2018
Mathematics

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Sapphire Island is open 7 days a week. The park has 8 ticket booths, and each booth has a ticket seller from 10:00 a.m. to 5 p.m. On average, ticket sellers work 30 hours per week.

Write and solve an equation that can be used to find t, the minimum number of sellers the park needs. Interpret the solution.

The park plans to hire 20% more than the minimum number of ticket sellers needed in order to account for sickness, vacation, and lunch breaks. How many ticket sellers should the park hire?

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Sicista Sicista · Answer 1 · 2018-09-15T13:59:52+02:00

Minimum number of ticket seller needed is 14 and if the park want to hire 20% more seller, then the number of seller will be 17.

Explanation

Minimum number of ticket seller is [tex]t[/tex] and each seller work 30 hours per week on average.

So, the total working hours of all seller in a week [tex]=30t[/tex] hours.

The park has 8 ticket booths, and each booth has a ticket seller from 10:00 a.m. to 5 p.m. That means in each booth, the sellers work for 7 hours per day.

So, in 8 booths, total working hours per day [tex]=(7*8)hours= 56 hours[/tex] and total working hours in a week [tex]=(56*7) hours = 392 hours[/tex]

Thus the equation will be...

[tex]30t= 392 \\ \\ t=\frac{392}{30}=13.06666.....[/tex]

As the number of seller can't be in decimal, so the minimum number of ticket seller will be 14.

If the park plans to hire 20% more than the minimum number of ticket sellers, then the number of ticket seller will be: [tex]14+(14*0.20)=14+2.8=16.8[/tex] ≅ 17.