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Question 845209: A number is 6 greater than 1/2 another number. The sum is 21, find the 2 numbers.
Answer by pmesler(52)   (Show Source):
You can put this solution on YOUR website! Let x = some number
Let y = the second number.
Therefore x = (y/2 + 6).
The problem says that x+y = 21.
All we have to do is substitute what we know x is into the equation and solve for y.
Therefore x+y = 21 becomes
(y/2 + 6) + y = 21
Now we need to isolate the y on the left side, but before we do that we need to combine like terms. We can't combine the y terms until both y's share the same denominator. To do this we need to multiply the second y by 2/2. That will give us the following:
(y/2 + 6) + y(2/2) = 21
We can multiply by 2/2 because 2/2 = 1 and multiplying anything by 1 does not change the value of the number. All we're doing is changing the form, not the value of the expression.
Our new equation is this:
(y/2 + 6) + (2y/2) = 21
Now we can combine the y terms and we get
3y/2 + 6 = 21.
Subtract 6 from both sides to simplify.
3y/2 = 15
Now to get y by itself we need to multitply both sides by the reciprocal of 3/2 which is 2/3. We do this so the numerator and denominators divide out and all we are left with is y.
(2/3)(3y/2) = 15(2/3).
y = 15 * 2/3
y = 30/3
y = 10. Now that we know that y = 10, it will be simple to find x.
x as you remember is (y/2 + 6)
Therefore x = (10/2 + 6)
x = 5 + 6
x = 11.
This checks out since 11 + 10 = 21.
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