SOLUTION: Efendi can buy an exact number of footballs with RM120. However, if the price of the football is reduced by RM6, he can buy an extra football. Determine the original price of the f

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Question 241561: Efendi can buy an exact number of footballs with RM120. However, if the price of the football is reduced by RM6, he can buy an extra football. Determine the original price of the football.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
RM = Malaysian Ringgit

x = number of footballs that can be bought for 120 rm.

120/x = price of one football.

reduce price of one football by 6 rm.

price of one football becomes (120/x) - 6

now you can buy one extra football for the same price as before (120 rm).

x * (120/x) = 120

(x+1) * ((120/x)-6) = 120

since they both equal to 120 then they are equal to each other.

x * (120/x) = (x+1) * ((120/x)-6)

multiply both sides by x to get:

x * 120 = (x + 1) * ((120 - 6x))

simplify by removing parentheses to get:

120*x = 120*x - 6x^2 + 120 - 6x

subtract 120*x from both sides to get:

120*x - 120*x - 6x^2 + 120 - 6x = 0

combine like terms to get:

-6x^2 + 120 - 6x = 0

multiply both sides by -1 to get:

6x^2 - 120 + 6x = 0

reorder terms on left side of equation to get:

6x^2 + 6x - 120 = 0

divide both sides by 6 to get:

x^2 + x - 20 = 0

factor to get:

(x+5) * (x-4) = 0

solve for x to get:

x = -5 or x = 4

x can't be negative so x = 4

Efendi buys 4 footballs for 120 rm.

he pays 30 rm apiece because 4 * 30 = 120.

price is reduced by 6 rm apiece.

price becomes 24 rm apiece.

he can now buy 5 footballs at 24 rm apiece because 5 * 24 = 120.