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The product of two positive numbers is 750. The first number is 5 less than the second number. The equation x(x – 5) = 750 can be used to find x, the value of the greater number.

What is the value of the greater number?

a. 15
b. 25
c. 30
d. 50

Relax

Respuesta :

irspow
ab=750 and a=b-5, using this value of a in the original equation gives you:

(b-5)b=750

b^2-5b=750

b^2-5b-750=0

b^2-30b+25b-750=0

b(b-30)+25(b-30)=0

(b+25)(b-30)=0

b=30 

Answer:

c. 30

Step-by-step explanation:

Here x represents the greater number or second number,

Since, The smaller number is 5 less than the greater number,

Thus, the smaller number = (x - 5)

Given,

The product of x and (x-5) is 750

⇒ x(x-5) = 750

[tex]x^2-5x=750[/tex]    ( By associative property )

[tex]x^2-5x-750=0[/tex]    ( By subtracting 750 on both sides )

[tex]x^2-(30-25)x-750=0[/tex]    ( By middle term splitting )

[tex]x^2-30x+25x-750=0[/tex]    

[tex]x(x-30)+25(x-30)=0[/tex]

[tex](x-30)(x+25)=0[/tex]

[tex]\implies x = 30\text{ or } x = -25[/tex]

But, both numbers are positive

⇒ x can not be negative in the given question.

Hence, the value of greater number is 30.

Option C is correct.

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