Lesson 4

Self-Check 2 and Self-Check 3 provide extra practice for applications of linear relations. Check your skills by doing the following self-checks.

Self-Check 2

The mass of a beaker and ethanol (M) is recorded when the beaker contains varying volumes of ethanol (v). The results of the experiment are recorded in the table. The beaker can hold a maximum of 1000 mL of ethanol.

Measurements may be assumed to be correct to the nearest millilitre (mL) and to the nearest gram (g).

Graph the relation, and respond to the following questions.

1. Assuming this pattern continues, determine the mass of the beaker and ethanol when 250 mL of ethanol is present. Answer
2. What volume of ethanol is in the beaker if the total mass is 450 g? Answer
3. When the volume of ethanol is 700 mL, determine the mass of the ethanol alone. Answer
4. Find an equation that relates the mass of the beaker and ethanol to the volume of ethanol. Answer

Self-Check 3

A small business makes ball caps and sells the caps to stores. Each ball cap costs $5 to make. The fixed monthly costs of the business, such as rent, salaries, and insurance, are $4000. The business sells the ball caps to the stores for $15 each. An equation to represent the cost (y) of making x ball caps is y = 5x + 4000. An equation to represent the revenue (y) of selling x ball caps is y = 15x.

1. Complete two tables of values similar to the tables shown. Answer
   
   

   COST: y = 5x + 4000
   Ball Caps (x)	Cost (y)
   0
   100
   200
   300

   
   

   REVENUE: y = 15x
   Ball Caps (x)	Revenue (y)
   0
   100
   200
   300

   
   profit = revenue − cost
2. Calculate the profit when 600 ball caps are sold. Answer
3. Calculate the profit when 150 ball caps are sold. Answer
4. The break-even point is when the revenue is equal to the cost, and thus the profit is 0. Calculate the break-even point using
   1. your tables from question 1 Answer
   2. the equations provided Answer