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Question 515423: the sum of two numbers is 14. if one of the numbers is doubled, the sum will become 22. what are the numbers?
Answer by drcole(72)   (Show Source):
You can put this solution on YOUR website! Let x and y be the two numbers. Then the sum of the two numbers is x + y, which we know is 14. This gives us the algebraic equation:
x + y = 14
Now, let's double one of the numbers (it doesn't matter which): x becomes 2x. The new sum is therefore 2x + y, which we know is 22, giving us a second algebraic equation:
2x + y = 22
Now we have two linear equations in two unknowns. We'll solve this system using the substitution method. First, we'll solve the first equation for y:
x + y = 14
y = 14 - x (subtract x from both sides)
Now we'll substitute 14 - x for y in the second equation and solve for y:
2x + y = 22
2x + (14 - x) = 22 (substitute 14 - x for y)
x + 14 = 22 (combine like terms)
x = 8 (subtract 14 from both sides)
Now we know that x = 8, and we substitute back into the expression we got for y to find y:
y = 14 - x = 14 - 8 = 6
So our solution is x = 8 and y = 6. Let's see if our solution makes sense. The sum of our two numbers is 8 + 6 = 14, which works. If we double x, we get 16, and the sum of 16 + 6 = 22, which also works. So our solution is correct.
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