Principles of Mathematics - MPM1DP

Unit 3: Linear Relations

Activity 9: Partial Variation

Content

Partial variation is a term used to describe a situation where a component is direct variation and a component is fixed. For example: If a fundraising dinner was being held, the cost would include hall rental and the price of each person’s meal. The hall rental would be your fixed cost. The cost of the meals varies according to the number of people attending.

Example: Fundraising Dinner

If you remember, the Parent Council is having a fundraising dinner. The cost of renting the hall is $425. The cost of each meal is $18.

What is the algebraic model or equation of this situation? Draw the graph of the equation. How much will the dinner cost the Parent Council if 100 people attend? How much will the dinner cost the Parent Council if 350 people attend?

Solution:

1. If C represents the total cost and n represents the number of people, the equation representing the cost is C = 18n + 425.
   

   Hint: To draw the line in Geometer’s Sketchpad, first find two points on the line. Use the point tool in Geometer’s Sketchpad and plot these points. Highlight the points, then go to Construct, Line.

2. 
   

   Note: in partial variation the line doesn’t cross the y-axis at the origin. In this example, the graph starts at (0, 425).

3. By substituting into the equation, the cost for 100 participants is C = 18(100) + 425. The cost is $2225.
4. The cost for 350 participants is C = 18(350) + 425. The cost is $6725.

Questions

1. Write the equation that represents each of the following situations. State whether the equation represents partial or direct variation.
   1. A taxi driver charges $6 plus $.05 per km
   2. Dave charges $12 per hour to cut your lawn
   3. A submarine rises from a depth of 5000 m to the surface at a rate of 10 metres per minute.
   4. Coffee costs $1.79 a cup.
   5. A furnace repair company charges $68 for a home visit. If repairs are needed there is an addition charge of $50 per hour.

   Answer

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