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O lvl E Maths: Algebraic Manipulation

RGS P2 Prelims 1997 Q4

A farmer bought 240 fruit bushes to plant in a field. He planted x rows, each containing the same number of bushes.

(a) Write down an expression, in terms of x, for the number of bushes in each row.

A second farmer bought 252 bushes, and he planted them in (x + 3) rows.
(b) Write down an expression for the number of bushes he planted in each row.

(c) Given that the first farmer had two bushes per row more than the second farmer, form an equation in x and show that it reduces to

x² + 9x - 360 = 0

(d) Solve this equation to find the number of bushes the first farmer had in each row.

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Answer:

(a) Number of bushes in each row = 240 / x

(b) Number of pushes planted in each row = 252 / (x + 3)

(c) 240 / x - 252 / (x + 3) = 2
Multiply by x(x + 3) throughout
240 (x + 3) - 252x = 2x (x + 3)
240x + 720 - 252x = 2x² + 6x
2x² + 18x - 720 = 0

Divide by 2 throughout
x² + 9x - 360 = 0 (shown)


(d) x² + 9x - 360 = 0
(x - 15)(x + 24) = 0
x = 15 or x = -24 (reject as x must be positive)

Hence, number of bushes the first farmer had in each row is 15



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