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Pepsi [2]
3 years ago
14

Find three consecutive even integers such that 3 times the first is 26 less than twice the sum of the last two

Mathematics
1 answer:
Dimas [21]3 years ago
4 0
Let's say our first integer is "a".

how to get the next consecutive EVEN integer?  well, just add or subtract 2 from it, therefore, the second consecutive integer will be "a + 2".

and the next after that, will then be (a + 2) + 2, or "a + 4".

so those are are 3 integers, a           a + 2           a+4

notice that, from any even or odd integer, if you hop twice either forwards or backwards, you'll land on another even or odd integer respectively.

2 + 2 is 4, or 8 + 2 is 10  some even ones

3 + 2 is 5, or 13 + 2 is 15, some odd ones

\bf \stackrel{\textit{3 times the first}}{3a}~~=~~\stackrel{\textit{26 less than twice the sum of the others}}{2[~(a+2)+(a+4)~]~~~-26}
\\\\\\
3a=2[~2a+6~]-26\implies 3a=4a+12-26\implies 3a=4a-14
\\\\\\
0=a-14\implies 14=a

what are the other two consecutive integers?  well, a + 2 and a + 4.
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