Question

The product of two successive integral multiple of 5 is 300 determine the multiple?

Answer 1

Question:

The product of two successive integral multiples of 5 is 300 then determine the multiples.

Note:

Two successive integral multiples of 5 differs by 5.

Solution:

Let a multiple of 5 be x , then the next multiple of 5 will be (x+5).

Now;

According to the question the product of these two successive multiples is 300.

Thus;

=> x(x + 5) = 300

=> x^2 + 5x = 300

=> x^2 + 5x - 300 = 0

=> x^2 + 20x - 15x - 300 = 0

=> x(x + 20) - 15(x + 20) = 0

=> (x + 20)(x - 15) = 0

=> x = - 20 , 15.

Case(1).

If x = - 20

Then (x+5) = - 20 + 5 = - 15

Product = (- 20)(- 15) = 300

Case(2)

If x = 15

Then (x+5) = 15 + 5 = 20

Product = 15•20 = 300

Hence,

Two such pairs are possible :

(15 and 20) & (-15 and -20)

Answer 2

SOLUTION:-

Given:

The product of two successive integral multiple of 5 is 300.

To find:

The multiples.

Explanation:

Assume the successive multiples of 5 be R, R+5.

•First number be R.

•Second number be R+5.

According to the question:

=) (R)(R+5)=300

=) R² + 5R=300

=) R² +5R-300=0

=) R²+20R -15R -300=0

=) R(R+20) -15(R+20)=0

=) (R+20)(R-15)=0

=) R+20=0 or R-15=0

=) R= -20 or R=15

Here, negative value not acceptable.

So,

R=15

• First number is 15
• Second number is 5+15= 20

Thus,

The two successive multiples of 5 whose product is 300 are 15 & 20.

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