A man bought a certain number of golf balls for RM 20. If each ball has costed 20 cents less, he could have bought five more for the same money. How many golf balls did he buy?​

Answer:

He bought 20 balls

Step-by-step explanation:

Cost of a certain number of golf balls = $20

Let 1 golf ball cost $x

This means number of balls bought = 20 / x

If each ball has costed 20 cents less;

Converting 20 cents to dollars = $0.2

$x - $0.2

he could have bought five more for the same money.

Number of balls = 20/x + 5

Using the formulae;

Cost of 1 ball * Number of balls bought = Amount spent

(x-0.2) (20/x + 5) = 20

Expanding the expression;

x(20/x + 5) - 0.2(20/x + 5) = 20

20 + 5x - 4/x - 1 = 20

19 + 5x - 4/x = 20

5x - 4/x = 1

Multiplying all through by x

5x^2 - 4 = x

5x^2  - x - 4 = 0

(5x + 4)(x - 1) = 0

x = 1 or -4/5

-4/5 is unrealistic hence the correct value is;

x = $1

He bought 20 balls;  20 / x = 20 / 1 = 20

The reduction in the price of each ball increases the number of balls the man can buy at RM 20.

The number of balls he bought is 20 balls.

Reasons:

The given parameters are;

The amount the man bought the golf balls = RM 20

The number of golf balls he could have bought if each ball costs 20 cents less = 5 more balls

Let the number of balls the man bought = x

Let the price of each ball be m

We have;

m × x = 20

(x + 5)·(m - 0.20) = 20

Therefore, we get;

[tex]m = \dfrac{20}{x}[/tex]

Which gives;

[tex]\left(x + 5 \right) \cdot \left(\dfrac{20}{x} - 0.20\right) = 20[/tex]

[tex]-\dfrac{\left(0.2 \cdot x^2- 19 \cdot x - 100\right)}{x} = 20[/tex]

20·x = -0.2·x² + 19·x + 100

0.2·x² + x - 100 = 0

x² + 5·x - 500 = 0

(x + 25)·(x - 20)

x = 20

The number of balls he bought, x = 20 balls

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