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

Answer:

let the two number be x and y.

Given: the product of two numbers is 450.

then:  $x\times y =450$                        ......[1]

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

i.e, $y=\frac{1}{2}x$

Substitute this in equation [1];

$x \times \frac{1}{2}x =450$

or

$\frac{1}{2}x^2 = 450$                  [∴$x^a \times x^b =x^{a+b}$]

Multiply both sides by 2; we get

$x^2 =450 \times 2$

or

$x^2=900$

or

$x=\sqrt{900} =30$

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

$30 \times y=450$

Divide by 30 from both the sides, we get;

$y = \frac{450}{30}=15$

Therefore, the equation $\frac{1}{2}x^2 = 450$ which can be used to find the value of x.

The greater number is x = 30.

Answer 2

The equation is used to find x is;

$\rm x^2=900$

The value of the greater number x is 30.

Given

The product of the two numbers is 450.

The first number is half the second number.

Let the first number be x and the second number be y.

The product of the two numbers is 450.

$\rm x\times y = 450$

The first number is half the second number.

$\rm x = \dfrac{1}{2} y$

Substitute the value of x in equation 1 from equation 2

$\rm x \times y = 450\\\\x \times \dfrac{1}{2}x = 450\\\\x^2 = 450 \times 2\\\\x^2=900\\\\x=30$

Substitute the value of x in equation 1

$\rm x\times y=450\\\\30 \times y = 450\\\\y = \dfrac{450}{30}\\\\y = 15$

Hence, the value of the greater number x is 30.

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