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what number whose sum of its digit is 26, becomes 6000 when rounded to the nearest thousands? lists 3 answers

Sagot :

PlanetMech

Answer:

  • 5993
  • 5984
  • 5975

Step-by-step explanation:

Word Problem

In order to solve the given word problem, let's first list down the given.

Given:

Let:  

w = the first  digit

x = the second digit

y = the third digit

z = the fourth digit

Analyzing the given word problem, in order to find out the digits that comprise the given number it needs to satisfy 2 conditions:

Conditions:

  • Sum of its digit is 26

thus,

w + x + y + z = 26

  • becomes 6000 when rounded to the nearest digit.

thus,

wxyz  ≤ 6000

Solution:

Let's list down four digits that when you add it the sum would be 26, considering that when you combine the digits the answer will be close to 6000 when it is rounded up:

First digit:

w = 5 (I will automatically choose 5 so that the thousands digit would start close to 6000)

x = 9

lets stop here for a bit and add the digits up in order to find out how much more is needed to sum up to 26.

5 + 9 = 14

26 - 14 = 12

thus the remaining digits for the tens and ones shoud be equal to 12

therefore the remaining digits are:

y = 9 (to maximize the given condition)

12 - 9 = 3

thus,

z= 3

Hence;

The first set of numbers would be:

5993

Checking:

  • Does the digit sum up to 26?

5 + 9 + 9 + 3 = 26

26 = 26

  • Is it close to 6000 when rounded up to the nearest thousands?

5993 rounded up to the nearest thousands is 6000

Therefore;

5993 satisfies the given conditions.

The process would just continue to the next two set of numbers.

w = 5 (to maximize to the given conditions)

x = 9 (to maximize to maximize to the given conditions)

y = 8 (similar case from above we need to maximize the remaining digits so that it would be equal to 26 and close to 6000 when rounded up. Since 9 is already given we step down to the lower digit which is 8)

z = 4 (because 12 - 8 = 4)

Hence;

The second set of numbers would be:

5984

Checking:

  • Does the digit sum up to 26?

5 + 9 + 8 + 4 = 26

26 = 26

  • Is it close to 6000 when rounded up to the nearest thousands?

5984 rounded up to the nearest thousands is 6000

Therefore;

5984 satisfies the given conditions.

The last set of numbers would be:

w = 5 (to maximize to the given conditions)

x = 9 (to maximize to the given conditions)

y = 7  (similar case from above we need to maximize the remaining digits so that it would be equal to 26 and close to 6000 when rounded up. Since 9 and 8 is already given we step down to the lower digit which is 7)

z = 5 (because 12 - 7 = 5)

Hence;

The first set of numbers would be:

5975

Checking:

  • Does the digit sum up to 26?

5 + 9 + 7 + 5 = 26

26 = 26

  • Is it close to 6000 when rounded up to the nearest thousands?

5975 rounded up to the nearest thousands is 6000

Therefore;

5975 satisfies the given conditions.

I hope the explanation made sense to you.

For solving word problems, you may refer to the below link:

https://brainly.ph/question/40999

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