Question 101793: Find two numbers whose sum is 62 and whose difference is 6.
Found 2 solutions by bucky, Fombitz:
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You have two unknown numbers. Call one of these numbers x and the other one y.
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The problem tells you that the sum of these two numbers, x and y, is equal to 62. Write this
in equation form as:
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x + y = 62
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The problem also tells you that the difference between x and y is 6. Write this in equation
form as:
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x - y = 6
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Notice that one of the equations contains a plus y and the other equation contains a minus y.
Suppose we add the two equations together. The +y will cancel the -y and we will be left with
just the variable x. So let's write the two equations as:
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x + y = 62 and
x - y = 6
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Add them vertically. The +x plus the +x gives you +2x. The +y and the -y cancel each other.
And the 62 plus 6 equals 68. So when we add the columns vertically we are left with:
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2x = 68
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Solve for x by dividing both sides of this equation by 2. When you do, the result is:
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x = 68/2 = 34
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So one of the numbers is 34. Since the two numbers have to add up to be 62 you can find
the value of the other number by subtracting 34 from 62. And 62 minus 34 is 28.
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So the two numbers you are looking for are 28 and 34. They check because their difference
is 6 and their sum is 62.
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Hope this helps you to see how to do this problem. When you are looking for two unknowns you
will need two independent equations to find them.
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Answer by Fombitz(32388)  (Show Source):
You can put this solution on YOUR website! Let’s call the first number A, the second number B.
(1) A + B = 62
(2) A – B = 6
Let’s use equation (2) to solve for B in terms of A and then we’ll substitute in equation (1) to solve for A.
(2) A – B = 6
A – B + B = 6 + B Use the additive inverse of (-B) or B
A = 6 + B Simplify
-6 + A = -6 + 6 + B Use the additive inverse of (6) or -6
-6 + A = B or
(3) B = A – 6. We’ll call that equation (3), that’s B in terms of A. Really it’s equation (2) re-arranged.
Now let’s use this answer in equation (1)
(1) A + B = 62
A + (A - 6) = 62 Plug in your value for B.
2A - 6 = 62
2A – 6 + 6 = 62 + 6 Use the additive inverse of (-6) or 6
2A = 68
2A/2=68/2 Use the multiplicative inverse of (2) or 1/2
A=34 Use your answer for A in (1),(2), or (3) and solve for B.
Let’s use (3), it’s most direct.
(3) B = A – 6
B = 34 - 6
B = 28
The answers are A=34, B=28.
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