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?

Answer 1

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?

The first number is half the second number, then:
The second number is the greater number: x
Let be:
The first number: y

The product of two numbers is 450:
xy=450

The first number is half the second number:
y=x/2

The equation of the product can be used to find x:
Replacing y by x/2 in the equation of the product:
x(x/2)=450
Solving for x:
x^2/2=450
2(x^2/2)=2(450)
x^2=900
sqrt(x^2)=sqrt(900)
x=30

y=x/2=30/2→y=15

Answer 2

Given:
product of 2 numbers is 450.
first number is half the second number.

Let us make our own equation based on the given data.

Let x and y be the two numbers.

y * x = 450

y is the 1st number. It is said that it is half the second number, x.

y = 1/2 * x = x/2

Let us substitute y of the 1st equation by its value in the second equation.

x/2 * x = 450

x² / 2 = 450
x² = 450 * 2
x² = 900
√x² = √900
x = 30

The value of x, the 2nd number, is 30.

y = x/2 = 30/2 = 15

The value of y, the 1st number, is 15.

To check:

y * x = 450
15 * 30 = 450

450 = 450