Question

The product of two numbers is 450. the first number is half the second number. which equation can be used to find x, the greater number? = 450 225x2 = 0 x2 = 450 450x2 = 0

Answer 1

let the two number be x and y.

Given: the product of two numbers is 450.

then:
`x* y =450` ......[1]

Also from the given condition that; the first number is half the second number. Also, x>y.

i.e,
`y=(1)/(2)x`

Substitute this in equation [1];

`x * (1)/(2)x =450`

or

`(1)/(2)x^2 = 450` [∴
`x^a * x^b =x^(a+b)`]

Multiply both sides by 2; we get

`x^2 =450 * 2`

or

`x^2=900`

or

`x=√(900) =30`

Now, substitute this x value in [1], to solve for y;

`30 * y=450`

Divide by 30 from both the sides, we get;

`y = (450)/(30)=15`

Therefore, the equation
`(1)/(2)x^2 = 450` which can be used to find the value of x.

The greater number is x = 30.