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Thepotemich [5.8K]
3 years ago
7

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

Mathematics
2 answers:
Firlakuza [10]3 years ago
6 0

Answer:

  • (25, 400) or (-25, - 400)

Step-by-step explanation:

Let the numbers be x and y.

<u>We have:</u>

  • y = 16x
  • xy = 10000

<u>Substitute y and solve for x:</u>

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

<u>Then y is:</u>

  • y = ± 25*16 = ± 400

<u>The numbers are:</u>

  • 25 and 400 or -25 and - 400
Simora [160]3 years ago
5 0

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

<h2>➯Question:</h2>

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

<h2>Answer:</h2>

  • Both numbers are 25 and 400.

<h3>Step By Step Explanation:</h3>

<h3>Given that:</h3>

  • The product of two numbers is 10000.

  • One number is 16 times the other number.

<h3>To Find:</h3>

  • Both numbers?

<h3>Solution:</h3>

  • 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.

<h3>According to the Question :</h3>

\sf↦ Product ~of ~numbers = 10000\\\\↦ n × 16n = 10000\\\\↦ 16n² = 10000\\\\↦ n² = \sf \dfrac{10000}{16}\\\\↦ \sf n = \sqrt{\dfrac{10000}{16}}\\\\↦ \sf n = \sqrt{\dfrac{100\:\times\:100}{4\:\times\:4}}\\\\↦ \sf n = {\cancel{\dfrac{100}{4}}}\\\\➦\pmb{\underline{\boxed{\sf{\pink{n = 25}}}}}

<h3>Hence,</h3>

  • 1st number = n = 25

  • 2nd number = 16n = 16 × 25 = 400

<h3>∴ Hence, both numbers are 25 and 400.</h3>

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

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