SOLUTION: 1) find 4 consecutive even integers such that the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3. 2) Find three

Question 155748: 1) find 4 consecutive even integers such that the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3.
2) Find three consecutive odd integers such that 4 less than twice the second has the same value as three times the number that is one more that the third.

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1) find 4 consecutive even integers such that the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3.
:
4 consecutive integers: x, x+2, x+4, x+6
:
Write an equation for the statement:
"the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3."
= 3
:
= 3
:
= 3
Multiply both sides by (3x+18)
11x + 26 = 3(3x + 18)
:
11x + 26 = 9x + 54
:
11x - 9x = 54 - 26
:
2x = 28
x =
x = 14
:
The four numbers: 14, 16, 18, 20
:
Check the solutions in the statement:
"the sum of twice the first, five times the second and four times the third divided by three times the fourth equals 3."
= 3
= 3
= 3
:
:
2) Find three consecutive odd integers such that 4 less than twice the second has the same value as three times the number that is one more that the third.
:
We have: x, (x+2), (x+4) as the three consecutive odd numbers
:
2(x+2)- 4 = 3(x+4+1)
2x + 4 - 4 = 3(x+5)
2x = 3x + 15
2x = 3x = 15
-x = 15
x = -15
;
The numbers: -15, -13, -11
:
;
Check:
2(-13) - 4 = 3(-11+1)
-26 - 4 = 3(-10)
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