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Question 588550: The sum of 2 numbers is 77. Their difference is 7. Find the 2 numbers
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let X and Y represent the two unknown numbers. Since we have two unknowns, we need two independent equations to solve for them.
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The problem tells you that the sum of these two numbers equals 77. So let's write an equation that says that:
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X + Y = 77
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The problem also tells you that the difference between the two numbers is 7. Now let's write an equation that says that:
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X - Y = 7
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These are the two equations we need, and they will allow us to find values for X and Y. One of the ways we can solve a pair of equations such as this is by variable elimination. If we can add or subtract the two equations and in doing so one of the variables disappears, we can solve the new equations for the other variable. Let's write the equations one above the other like this:
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X + Y = 77
X - Y = 7
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Notice that if we add the two equations vertically that the +Y and the -Y cancel each other so they disappear. The X in the top equation adds to the X in the lower equation to give 2X and on the other sides of the two equations the 77 adds to the 7 to give 84. So after adding the two equations vertically we are left with a new equation:
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2X = 84
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We now solve for X by dividing both sides of this new equation by 2 to get:
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X = 42
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Next we can go back to either of the two original equations we wrote and in the one that we choose, we can substitute 42 for X and then solve for Y. Let's select the first of our two original equations:
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X + Y = 77
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Substitute 42 for X and this becomes:
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42 + Y = 77
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Solve for Y by subtracting 42 from both sides of this equation. When we do that the 42 on the left side disappears and we are left with:
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Y = 77 - 42 = 35
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That means that we know the two unknown numbers are 42 and 35. You can check to verify this by adding them to ensure that their total is 77 and then subtracting them to see that the difference is 7.
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Hope this helps you to understand the problem a little more.
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