solve the following problem

Question

a) Which is more economical: purchasing the large size sack of beans at 5 kilograms for $24, or purchasing the regular size bag at 86 grams for $1.60?

 

b) Joe buys 120 pens which cost 95 cents per dozen. He can make a gift box that uses four pens, a 5 cent ribbon and 10 cent box. He sell each gift box for $2.25. What is Joe’s total profit?

 

c) A restaurant allows customers to choose any two different vegetables for the lunch special from the set, {corn, peas, carrots, okra, squash}. How many different ways are there to choose?

Answer 1

(a)  $1.60/86 g = 160 cents/86 g

 

      $24/5 kg = $24/5000 g = 2400 cents/5000 g = 24 cents/50 g

 

      = 48 cents/100 g = 0.48 cents/gram = 0.48(86) cents/86 g 

 

                                                            < 160 cents/86 g

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 (b)    profit = revenue - cost (P = profit; R = revenue; C = cost)

 

         per box (4 pens):  R = $2.25 

         for 120 pens (30 boxes):  R = 30($2.25) = $67.50

         for 12 pens (3 boxes):  C = $0.95

 

         for 120 pens (30 boxes):  C = $9.50

 

         for 120 pens (30 boxes):

                               cost of ribbons = ($0.05/box)(30 boxes) = $1.50

 

         for 120 pens (30 boxes):  

                                 cost of boxes = ($0.10/box)(30 boxes) = $3.00

 

         total cost (30 boxes):  C = $9.50 + $1.50 + $3.00 = $14.00

 

         profit (30 boxes): P = R - C = $67.50 - $14.00 = $53.50 

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(c) corn, peas, carrots, okra, squash --- 2 veggies

 

     corn, peas         peas, carrots      carrots, okra       okra, squash          corn, carrots      peas, okra         carrots, squash

     corn, okra          peas squash         

     corn, squash

 

     total = 4  + 3 + 2 + 1 = 10