# Question

Ps help. Many tks and God Bless:)

A shopkeeper bought x pencil cases for \$108

(a) Write down an expression in terms of x, for the cost price, in dollars, of one pencil case

(b) the shopkeeper sold 10 pencil cases at a profit of \$1.50 each and the remaining at \$7.50 per pencil case. Write an expression in terms of x, for the total amount of money received from the sale of the pencil cases.

(c) Given that he made a profit of \$12 from the sale, form an equation in x and show that it reduces to xsquared -24x +144=0. Hence find the number of pencil cases bought by the shopkeeper.

(a) Cost of each pencil case = \$108/x

(b)

Pencil case sold at \$1.50 profit => selling price = \$(108/x + 1.50) each

Number of pencil cases sold at \$7.50 each = (x – 10)

= 10(108/x + 1.5) + 7.5(x – 10)

= 1080/x + 15 + 7.5x – 75

= 1080/x + 7.5x – 60

(c)

Profit of \$12 => total collection = 108 + 12 = \$120

1080/x + 7.5x – 60 = 120

1080 + 7.5x2 – 60x = 120x

7.5x2 – 180x + 1080 = 0

x2 – 24x + 144 = 0

(x -12)(x – 12) = 0

(x – 12) = 0

x = 12

Check

Cost price = 108 / 12 = \$9

\$1.50 profit => selling price = 9 + 1.50 = \$10.50

10 x \$10.50 + 2 x \$7.50 = \$105 + \$15 = \$120

\$120 – \$108 = \$12 (profit)

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