Theory question 111
Inequalities(a) The profit, P, made by a retailer for selling y number of articles in a day is given by P = (3y2 − 9)/(y − 2) − 18/(y − 2)
(i) If $16.00 profit was made in a particular day, determine the number of articles sold.
(ii) On a particular day, no profit was made for sales of articles. Find the number of articles sold.
(b) Solve (5 + x)/6 + (4x − 1)/3 ≥ (3x + 2)/5
Show the model answer
Model answer
(a)(i) (3y² − 27)/(y − 2) = 16 ⇒ 3y² − 16y + 5 = 0 ⇒ (3y − 1)(y − 5) = 0 ⇒ y = 5 articles (y must be a whole number)
(ii) 3y² − 27 = 0 ⇒ y² = 9 ⇒ y = 3 articles
(b) Multiply by 30: 5(5 + x) + 10(4x − 1) ≥ 6(3x + 2) ⇒ 45x + 15 ≥ 18x + 12 ⇒ 27x ≥ −3 ⇒ x ≥ −1/9
Explanation
Combine the two fractions first; they share the denominator y − 2.