Please page up or page down and refresh the work if necessary.
A perfumed body spray is made up as follows:

• Hydrocarbon Propellent at 98%
• and a perfume disolved in an alcohol at 0.01 parts perfume in 1 part alcohol where "parts" shall mean "parts by weight".
• When applied all the propellent dissipates into the atmosphere and all the alcohol evapourates on contact with the skin.
• Assume that the container has a capacity of 5ml.
  and that the user will get 10 equal treatments at 10mg body spray per treatment.
• Costings

  	Raw Material	Cost
  	Perfume	R120/mg
  	Propellent	R0.5/mg
  	Alcohol	R2/mg

• Container : Made of solid gold or any suitable material. The price to be negotiated.
• Please use a scientific calculator and work to as many decimal places as possible for an accurate result ?.
• All these facts are hypothetical and are made as a basis for starting a new business.

1. How much perfume is left on the skin after 1 treatment.?  Solution 1
2. Determine the cost of the product in the 5ml container.  Solution 2
3. Determine the cost of 10l of the product  Solution 3
4. Determine the cost of 10l of the product rounded to the nearest whole number.  Solution 4
5. What are the tax implications of rounding to the nearest whole number?  Solution 5
6. Why is the perfumed alcohol defined in parts?  Solution 6
7. Notes for the Teacher

Solution 1

98
Propellent = 98% of 10mg = ——× 10 = 9.8mg
100
∴ 0.2mg perfumed alcohol is applied to the skin
Formulation for the perfumed alcohol
0.01 parts perfume : 1 part alcohol ⇒ 1part perfume : 100 parts alcohol "⇒" shall mean "implies" in this instance only.
1100
——×0.2mg perfume : ——×0.2mg alcohol
101101
ie mg perfume left on the skin : mg alcohol
Check using a scientific calculator (Casio fx-82MS - purchased 1976)
1.98019802×10⁻³ mg perfume + 0.198019802 mg alcohol ≅ 0.2mg perfumed alcohol (⍻ as expected)

Solution 2

Cost of the product in the 5ml container
10 treatments at 10mg body spray per treatment = 100mg body spray
98
Cost of Propellent = ——×100×0.5 = xxxxxxxxxx
100
100
Cost of the Alcohol = ——×2×2 = xxxxxxxxxxx
101
1
Cost of Perfume = ——×2×120 = xxxxxxxxxxx
101

Product	Cost in Rands to 8-10 decimal places
Propellent	######
Alcohol	######
Perfume	######
Cost	######

Solution 3

Cost of 10l of the product = 10×1000ml = 10000ml
5ml cost xxxxxxxxxx
∴ 10000ml cost xxxxxxxxxx

Solution 4

Cost of 10l perfumed body spray rounded to the second decimal place ≅ ##########
Cost of 10l perfumed body spray rounded to the nearest whole number ≅ ##########

Solution 5

The loss of 27c must be explained to the tax man on every 10l perfumed body spray sold
Assuming that the tax man only taxes on a profit ???.

Solution 6

The size or type of container has not yet been determined and the formulation for the Perfumed Alcohol should be independent
of the requirements of the container.
So if the company decides to use a 5ml or 10 ml or 20ml container
made of gold or silver or platinum the formula for the perfumed alcohol must not change.
i.e. 0.01 parts perfume : 1 part alcohol. or
1 part perfume : 100 parts alcohol which is easier to work with.

For the Teacher

1. JavaScript was used to avoid manual entry mistakes during the lesson.
   Javascript is not part of the syllabus.
2. Cascading Style Sheets were used to format the numerical analysis.
   Cascading Style Sheets are not part of the syllabus.
3. A <noscript> element is inserted into a <div> element
   to advise the student to enable JavaScript if necessary.
4. Some exercises are presented on a memory stick as a single file.
   So the separation of structure (HTML) , presentation (Cascading Style Sheets)
   and behaviour (JavaScript) is not possible as recommended by the World Wide Web Consortium (W3C)
5. Some programming languages provide automatic rounding to correct floating-point discrepancies but JavaScript does not.
   JavaScript only rounds to the nearest whole number.
   So care must be taken especially with monetary values to avoid erroneous results.
   The recommended procedure is to first multiply the floating-point value by 100,
   then perform the arithmetic operation and finally divide the result by 100
   to return to the same decimal value.
   num *= 100 ;
   num = Math.round(num);
   num/=100;
   otherwise use
   num = (Math.round(num*100))/100;