The larger of two consecutive integers is more than half the smaller integer. Find the numbers.
Let x = smallest integer
Let x + 1 = the larger of the two
The larger of the two = (1/2) (x) + x...The extra x came from the fact that the question said "...is more" The word more is associated with addition in word problems.
We get this:
2x + 2 = 3x
2 = 3x - 2x
2 = x
The first number is 2.
The second number would be x + 1 or 2 + 1 = 3.
The numbers are 2 and 3.
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How do we know that x = 2 is right?
We can plug x = 2 into the original equation and simplify.
If get the same answer on both sides of the equation, then we will know that x = 2 is correct.
THE PROVE:
....This is our original equation that was made from the information in the word problem.
= 3....It checks!
Since we got the same answer on both sides of the equation (3 = 3), this is our prove that
x = 2 is the correct answer, which led us to find the two consecutive numbers being 2 and 3.
Is this clear?