Question

A trader bought m apples for $12.

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 +1194 -3600/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