Question

A trader bought m apples for $12.
(a) Find an expression, in terms of m, for the cost, in cents, of each apple.
(b) It was found that 3 of the apples were bad, and could not be sold. The trader sold each remaining apple for 2 cents more than she paid for it.
Write down an expression, in terms of m, for the total sum she received from the sale of the apples.
(c) She made a profit of 96 cents from the sale of the apples.
Write down an equation to represent this information, and show that it simplifies to

${m}^{2} - 51m - 1800 = 0$
(d) Solve the equation
${m}^{2} - 51m - 1800 = 0.$
(e) Find the selling price of each apple.



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Answer 1

Answer:

a) total cost of m apples= $12 = 1200 cents

($1= 100cents, so $12= 12×100 cents)

cost of each apple= 1200/m

b) Number of apples sold= m-3

selling price of each apple= (1200/m) +2

Total sum received from sales:

$(\frac{1200}{m} + 2)(m - 3) \\ = \frac{1200}{m} (m) - 3( \frac{1200}{m}) + 2m - 3(2) \\ = 1200 - \frac{3600}{m} + 2m - 6 \\ = (2m + 1194 - \frac{3600}{m} ) \: cents$

c) profit= amount received- amount spent on buying apples

96= 2m [phone]/m -1200

2m -6 -96 -3600/m =0 (simplify, bring 96 over)

2m- 102 -3600/m =0

2m^2 -102m -3600 =0 (multiply by m on both sides)

m^2 -51m -1800 =0 (divide by 2 on both sides)

(shown)

d) m^2 -51m -1800=0

$x = \frac{ -b± \sqrt{{b}^{2} - 4ac } }{2a}$

Hence, using the above formula,

$m = \frac{ - ( -51)± \sqrt{( - 51) {}^{2} - 4(1)( - 1800) } }{2(1) } \\ m = \frac{51± \sqrt{9801} }{2} \\ m = 75 \: \: \: \: \: or \: \: \: \: \: m = - 24$

e) Thus, selling price of each apple

= 1200/75 +2

= 18 cents

This is found by substituting the value of m, which is 75, into the equation of the selling price of each apple which we found earlier in part b.

note: do not reject m= -24 in part d because you are simply solving the equation not finding out the number of apples the trader bought, m.

We ignore m= -24 in part e as it is not possible for the number of apples bought be a negative number