SOLUTION: the sum of two numbers is 50. the greater number is 12 more than the lesser number. what are the two numbers?

Question 591062: the sum of two numbers is 50. the greater number is 12 more than the lesser number. what are the two numbers?

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Let G represent the unknown greater number, and let L represent the unknown lesser number.
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Because there are two unknowns, G and L, we will need two separate equations in order to solve for these two unknown numbers.
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The problem tells us that the sum of the two unknown numbers is 50. So we can write one equation as:
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G + L = 50 <--- this is the first equation that we can use
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Next the problem tells us that 12 more that the lesser number is equal to the greater number. Therefore, we can write the equation:
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12 + L = G <--- this is the second equation that we can use
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We now have a system of two independent equations so we can solve for the two unknowns. Let's solve them by using substitution. We will solve our first equation for one of the unknowns in terms of the other. Then we will substitute that answer into the second equation and solve it.
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Let's begin by subtracting L from both sides of the first equation. That subtraction will make the L disappear from the left side and will make -L appear on the right side of this first equation. As a result the first equation becomes:
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G = 50 - L
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We now go to our second equation, and in it we replace G with its equivalent of 50 - L. This substitution makes the second equation become:
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12 + L = 50 - L
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We now have one equation that contains only one of the unknowns. So we can solve for that unknown.
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We start with:
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12 + L = 50 - L
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and we get rid of the - L on the right side by adding + L to both sides to get:
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12 + L + L = 50
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Next we get rid of the 12 on the left side by subtracting 12 from both sides to make the equation become:
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L + L = 50 - 12
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Do the addition on the left side and the subtraction on the right side to reduce the equation to:
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2L = 38
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Finally, solve for L by dividing both sides of this equation by 2 to get:
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L = 19
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That's one of the unknowns. The lesser number is 19. Then from the first equation that we found, we know that the sum of the two numbers is 50. So the greater number has to be 31 because 31 plus 19 equals 50.
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So our two unknown numbers are 19 and 31.
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You can check this by using the fact that the problem also tells us that the greater number is 12 more than the lesser number. And since 31 is 12 more than 19, we can be certain that our answer really is correct.
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I hope this helps you to understand this problem a little better.
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