Mathematics Questions and Answers

Total cost of production = N120.00

Labour Cost = \(\frac{70}{120}\) x \(\frac{360^o}{1}\)

= 210o

Number of boy's = 30

Number of girls = x

Mean of boys' score = 6, for girls = 8

Total score for boys = 30 x 6

Total score for both boys and girls = 468

180 + 8x = 468

x = \(\frac{288}{8}\)

= 36

Total yield = N3,700

Total amount invested = N 50,000

Let x be the amount invested at 6% interest and let y be the amount invested at 8% interest

then yield on x = \(\frac{6}{100}\) x and yield on y = \(\frac{8}{100}\)y

Hence, \(\frac{6}{100}\)x + \(\frac{8}{100}\)y

= 3,700.........(i)

x + y = 50,000........(ii)

6x + 8y = 370,000 x 1

x + y = 50,000 x 6

6x + 8y = 370,000.........(iii)

6x + 6y = 300,000........(iv)

eqn (iii) - eqn(2)

2y = 70,000

y = \(\frac{70,000}{2]\)

= 35,000

Money invested at 8% is N35,000

Let x represent the price of an orange and

y represent the number of oranges that can be bought

xy = 240k, y = \(\frac{240}{x}\).....(i)

If the price of an oranges is raised by \(\frac{1}{2}\)k per orange, number that can be bought for N240 is reduced by 16

Hence, y - 16 = \(\frac{240}{x + \frac{1}{2}\)

= \(\frac{480}{2x + 1}\)

= \(\frac{480}{2x + 1}\).....(ii)

subt. for y in eqn (ii) \(\frac{240}{x}\) - 16

= \(\frac{480}{2x + 1}\)

= \(\frac{240 - 16x}{x}\)

= \(\frac{480}{2x + 1}\)

= (240 - 16x)(2x + 1)

= 480x

= 480x + 240 - 32x² - 16

480x = 224 - 32x²

x² = 7

x = \(\sqrt{7}\)

= 2.5

= 2\(\frac{1}{2}\)k

Let the selling price(SP from P to Q be represented by x

i.e. SP = x

When SP = x at 10% profit

CP = \(\frac{100}{100}\) + 10 of x = \(\frac{100}{110}\) of x

when Q sells to R, SP = N209 at loss of 5%

Q's cost price = Q's selling price

CP = \(\frac{100}{95}\) x 209

= 220.00

x = 220

= \(\frac{2200}{11}\)

= 200

= N200.00