Home / Assignment Help / The waitress and hostess at a restaurant share the tips at the end of every shift. Between the two of them, they earn an average of $75 in tips. The waitress take $55 and the hostess takes $20. If they continue to earn money at this rate, how much will the waitress receive if they earn $300 at the end of their next shift?

The waitress and hostess at a restaurant share the tips at the end of every shift. Between the two of them, they earn an average of $75 in tips. The waitress take $55 and the hostess takes $20. If they continue to earn money at this rate, how much will the waitress receive if they earn $300 at the end of their next shift?

Answer:

3 hours.          

Step-by-step explanation:

Let x be the time taken by shoe repairman to repair one pair.

We have been given that his assistant, who takes twice as long to repair a pair of shoes. So time taken by his assistant to repair one pair of shoes would be 2x.

The number of pair of shoes repaired by repairman in one hour would be frac{1}{x}.

The number of pair of shoes repaired by assistant in one hour would be frac{1}{2x}.

We have been given that together they can fix 16 pairs of shoes in an eight-hour day. We can represent this information in an equation as:

frac{1}{x}+frac{1}{2x}=frac{8}{16}

frac{1}{x}+frac{1}{2x}=frac{1}{2}

Let us have a common denominator.

frac{2*1}{2*x}+frac{1}{2x}=frac{1}{2}

frac{2}{2x}+frac{1}{2x}=frac{1}{2}

frac{2+1}{2x}=frac{1}{2}

frac{3}{2x}=frac{1}{2}  

Upon cross multiplying our equation we will get,

2x*1=3*2

2x=3*2

frac{2x}{2}=frac{3*2}{2}

x=3

Therefore, it take 3 hours for the repairman to fix one pair of shoes by himself.

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