Answer :
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.
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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