Practice

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CHAPTER 8 Linear Applications

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Solutions

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CHAPTER 8 Linear Applications

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6: 1:8x 18 x 18 1:8 18 10 x 1:8 10 180 x 10 1000% 18

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1 is 125% of 2 4 8: 1 x 2 4 x 4 2 x 8 800% 1 2 is 800% of : 4 For some word problems, nothing more will be required of you than to substitute a given value into a formula, which is either given to you or is readily available The most di cult part of these problems will be to decide which variable the given quantity will be For example, the formula might look like R 8q and the value given to you is 440 Is R 440 or is q 440 The answer lies in the way the variables are described In R 8q, it might be that R represents revenue (in dollars) and q represents quantity (in units) sold of some item If 440 units were sold, what is the revenue Here 440 is q You would then solve R 8 440 If the revenue is $440, how many units were sold Here 440 is R, and you would solve 440 8q:

Examples

The cost formula for a manufacturer s product is C 5000 2x, where C is the cost (in dollars) and x is the number of units manufactured

CHAPTER 8 Linear Applications

(a) If no units are produced, what is the cost (b) If the manufacturer produces 3000 units, what is the cost (c) If the manufacturer has spent $16,000 on production, how many units were manufactured Answer these questions by substituting the numbers into the formula (a) If no units are produced, then x 0, and C 5000 2x becomes C 5000 2 0 5000 The cost is $5,000 (b) If the manufacturer produces 3000 units, then x 3000, and C 5000 2x becomes C 5000 2 3000 5000 6000 11;000 The manufacturer s cost would be $11,000 (c) The manufacturer s cost is $16,000, so C 16,000 Substitute C 16,000 into C 5000 2x to get 16;000 5000 2x 16,000 5000 2x 5000 5000 11,000 2x 11,000 x 2 5500 x There were 5500 units produced The pro t formula for a manufacturer s product is P 2x 4000 where x is the number of units sold and P is the pro t (in dollars) (a) What is the pro t when 12,000 units were sold (b) What is the loss when 1500 units were sold (c) How many units must be sold for the manufacturer to have a pro t of $3000 (d) How many units must be sold for the manufacturer to break even (This question could have been phrased, How many units must be sold in order for the manufacturer to cover its costs ) (a) If 12,000 units are sold, then x 12,000 The pro t equation then becomes P 2 12;000 4000 24;000 4000 20,000 The pro t is $20,000 (b) Think of a loss as a negative pro t When 1500 units are sold, P 2x 4000 becomes P 2 1500 4000 3000 4000 1000 The manufacturer loses $1000 when 1500 units are sold (c) If the pro t is $3000, then P 3000; P 2x 4000 becomes 3000 2x 4000