Question

The product of two numbers is 10000.If one number is 16 times the other numbers ,find the two numbers.​

Answer 1

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➯Question:

• The product of two numbers is 10000. If one number is 16 times the other numbers ,find the two numbers.

Answer:

• Both numbers are 25 and 400.

Step By Step Explanation:

Given that:

• The product of two numbers is 10000.

• One number is 16 times the other number.

To Find:

• Both numbers?

Solution:

• Let us consider that one number be n, in question it is stated that other number is 16 times the first number. Therefore, other number is 16n.

According to the Question :

`\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf (10000)/(16)\\\\↦ \sf n = \sqrt{(10000)/(16)}\\\\↦ \sf n = \sqrt{(100\:*\:100)/(4\:*\:4)}\\\\↦ \sf n = {\cancel{(100)/(4)}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}`

Hence,

• 1st number = n = 25

• 2nd number = 16n = 16 × 25 = 400

∴ Hence, both numbers are 25 and 400.

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Answer 2

• (25, 400) or (-25, - 400)

Explanation:

Let the numbers be x and y.

We have:

• y = 16x
• xy = 10000

Substitute y and solve for x:

• x(16x) = 10000
• 16x² = 10000
• x² = 10000/16
• x² = 625
• x = √625
• x = ± 25

Then y is:

• y = ± 25*16 = ± 400

The numbers are:

• 25 and 400 or -25 and - 400