SOLUTION: five consecutive integers have the property that the sum of the first 4 is exactly three times the fifth. find the sum of the nest five consecutive integers.

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Question 884949: five consecutive integers have the property that the sum of the first 4 is exactly three times the fifth. find the sum of the nest five consecutive integers.
Answer by JulietG(1812) About Me  (Show Source):
You can put this solution on YOUR website!
A + B + C + D = 3E
B = A+1 (because the numbers are consecutive)
C = A+2
D = A+3
E = A+4
Let's find A. Then, since everything is consecutive, we'll know the values of the others.
Substitute the known values from the bottom equations into the top.
A + B + C + D = 3E
A + (A+1) + (A+2) + (A+3) = 3(A+4)
Add / Distribute
4A + 6 = 3A + 12
Subtract 3A from each side
A + 6 = 12
Subtract 6 from each side
A = 6
If the first number is 6, the other numbers are 7,8,9, and 10
Let's prove it.
6+7+8+9 = 30
10 * 3 = 30
Success!