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one number is 6 more than another number, and their sum is 22. find the numbers.

Sagot :

Set the smaller one to x.  2x+6=22, so 2x=16.  Thus, x=8 and x+6=14, so 8 and 14 are our numbers.
akposevictor

If a number that is 6 more than another unknown number and the sum of both number gives 22, translating the word problem into algebraic expressions, the numbers are calculated as: 8 and 14.

First thing to do is to translate the word problem into algebraic expressions.

The first number:

Let x represent the unknown number which is another number.

The second number:

6 more than another number (x) will be translated as x + 6

The sum of both numbers:

Their sum equals 22. Therefore, we would have the following equation,

x + (x + 6) = 22

  • Solve for the value of x

[tex]x + x + 6 = 22[/tex]

  • Add like terms

[tex]2x + 6 = 22[/tex]

  • Subtract 6 from each side

[tex]2x = 22 - 6\\\\2x = 16[/tex]

  • Divide both sides by 2

x = 8

The first number is 8.

The second number would be:

x + 6

  • Plug in the value of x

8 + 6 = 14

Therefore, if a number that is 6 more than another unknown number and the sum of both number gives 22, translating the word problem into algebraic expressions, the numbers are calculated as: 8 and 14.

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