mini pizzas

Question

You are making 500 mini pizzas for a party you catering. each mini pizza requires 1 1/2 teaspoons of parmesan cheese. if 1 cup of parmesan cheese weighs 4 ounces, how many kilograms should you buy?

Answer 1

See Andrew M.'s step-by-step procedure for changing units.

 

To change units without changing the value, we use the multiplicative identity (that is, 1).

You will need to memorize (or look up) a few very handy conversions.  In this problem, we need:

  Volume:  cups, teaspoons

  Weight:  ounces, kilograms

And, we will use some intermediate ones that we know.

 

O.K., How much cheese should you buy?

    (500 mini-pizzas)*((1 1/2 teaspoons)/(1 mini-pizza))

    (500 mp)*((3/2 tp)/mp)                           [just saving space; now, multiply by 1]

    (500 mp)*((3/2 tp)/mp)*((1 cup)/(48 tp))    [1 cup = 48 tp; not many people know this]

    (500 mp)*((3/2 tp)/mp)*((1 cup)/(48 tp))*((4 oz )/((1 cup))      [given: 1 cup = 4 oz]

    (500)*(3/2)*(1/48)*(4) oz                           [cancel out units so far, but we could wait]

    (500)*(3/2)*(1/48)*(4 oz)*((1 pound)/(16 oz))*((1 kg)/(2.2 pound))    [good ones to memorize]

    (500)*(3/2)*(1/48)*(4)*(1/16)*(1/2.2) kg          [other units cancel out]

             (note:  I write expressions this way so I can paste into Excel]

    1.78 kg       [probably sold in whole kg, so buy 2 kg]

 

As you begin to see unit conversions, begin to memorize the most frequent ones (just like you did with 16 oz in 1 lb).

Answer 2

(1 1/2 tsp/pizza)(500 pizza) = 750 tsp of parmesan cheese

 

We need to find out how many cups we have ...

1 cup = 50 tsp  in metric units

Looking at our units:  teaspoons/(teaspoons/cup) = cup

so divide the number of teaspoons (750) by tsp/cup (50)

 

(750 tsp)/(50 tsp/cup) = 15 cups of parmesan cheese

 

Each cup of parmesan weighs 4 oz and we have 15 cups

15(4) = 60 oz of parmesan cheese

 

1 Ounce = 0.0283495231 Kilogram

 

(60 oz)(0.0283495231 kg/oz) = 1.7 kg

 

Hope this helps.  Good luck