(a) A manufacturer offers distributors a discount of $20%$ on any article bought and a further discount of $2\frac{1}{2}%$ for prompt payment. (i) if the marked price of an article is N25,000, find the total amount saved by adistributor for paying promptly. (ii) if a distributor pays N11,700 promptly for an article marked Nx, find the value of x. (b) Factorize $6y^{2} - 149y - 102$, hence solve the equation $6y^{2} - 149y - 102 = 0$.

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(a) A manufacturer offers distributors a discount of

20

on any article bought and a further discount of

2 \frac{1}{2}

for prompt payment.
(i) if the marked price of an article is N25,000, find the total amount saved by a distributor for paying promptly. (ii) if a distributor pays N11,700 promptly for an article marked Nx, find the value of x.
(b) Factorize

6 y^{2} - 149 y - 102

, hence solve the equation

6 y^{2} - 149 y - 102 = 0

Explanation

(a) (i) First discount = 20% of N25,000
=

\frac{20}{100} \times N 25, 000 = N 5, 000

Further discount for prompt payment =

2 \frac{1}{2}

of N25,000.
=

\frac{5}{200} \times N 25, 000 = N 625

∴ Total amount saved by distributor = N (5, 000 + 625)

N 5625

(ii) Total %age discount for prompt payment =

(20 + 2 \frac{1}{2})

Therefore, the distributor paid

(100

77 \frac{1}{2}

⟹ 77 \frac{1}{2}

x = \frac{11, 700 \times 200}{155}

N 15, 096.77

(b)

6 y^{2} - 149 y - 102

6 y^{2} - 153 y + 4 y - 102

3 y (2 y - 51) + 2 (2 y - 51)

(3 y + 2) (2 y - 51)

∴ 6 y^{2} - 149 y - 102 = 0 ⟹ (3 y + 2) (2 y - 51) = 0

3 y + 2 = 0 ⟹ 3 y = - 2

y = - \frac{2}{3}

2 y - 51 = 0 ⟹ 2 y = 51

y = 25 \frac{1}{2}

∴ y = - \frac{2}{3}; y = 25 \frac{1}{2}

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