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

The value of the greater number is 30.

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`

Answer 2

30

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