Question

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? 15 25 30 50

Answer 1

Answer:

  30

Step-by-step explanation:

You can try the answer choices to see what works.

  15·10 ≠ 750

  25·20 ≠ 750

  30·25 = 750 . . . . the larger number is 30

  50·45 ≠ 750

Answer 2

Answer:

The value of the greater number is 30.

Step-by-step explanation:

We need to find the values of x that satisfy the equation :

$x(x-5)=750$

Working with the equation ⇒

$x(x-5)=750$

$x^{2}-5x=750$

$x^{2}-5x-750=0$

Given an equation with the form

$ax^{2}+bx+c=0$

We can use the quadratic equation to find the values of x

$x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}$ and

$x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}$

With $a=1\\b=-5\\c=-750$ we replace in the equations of x1 and x2 ⇒

$x1=\frac{-(-5)+\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=30$

$x1=30$ is a solution of the equation $x^{2}-5x-750=0$

Now for x2 ⇒

$x2=\frac{-(-5)-\sqrt{(-5)^{2}-4.(1).(-750)}}{2.(1)}=-25$

$x2=-25$ is a solution of the equation $x^{2}-5x-750=0$

Given that both numbers are positive ⇒

$x>0$ and $(x-5)>0\\x>5$

Therefore, x2 is not a possible value for the greater number

The greater number is $x1=30$