Find four consecutive even integers such that the sum of twice thefirst, five times the second, and four times the third divided bythree times the fourth equals 3.

Corinne Woods

Corinne Woods

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2022-09-03

Find four consecutive even integers such that the sum of twice thefirst, five times the second, and four times the third divided bythree times the fourth equals 3.

Answer & Explanation

Javier Mathis

Javier Mathis

Beginner2022-09-04Added 7 answers

x=1st integer
x +2 =2nd integer and 2 because to go from 1 even # to the next you add 2 numbers
x+4 =3 integer
x+6 =4 integer
2x =twice the first
5(x+2) =5 times the 2nd
4(x+4) =4 times the 3rd
3(x+6) =3 times the 4th
2 x + 5 ( x + 2 ) + 4 ( x + 4 ) 3 ( x + 6 ) = 3
3(x+6)
expand all terms
2 x + 5 x + 10 + 4 x + 16 3 x + 18 = 3
combine like terms
11 x + 26 3 x + 18 = 3
cross multiply
11x+26=9x+54
subtract 9x from each side
2x+26=54
subtract 26 from each side
2x=28
divide each side by 2
x=14
the 4 numbers are14,16,18,20
check
twice the first=28
five times the 2nd = 80
four times the third = 72
three times the fourth = 60
(28+80+72)/60= 3
180/60=3
Brynn Collins

Brynn Collins

Beginner2022-09-05Added 1 answers

let the 4 consecutive even integers be denoted by : x , x+2, x+4,x+6
Using the information provided to us we can put this in an equationas:
[2x+5(x+2)+4(x+4) ]/ 3(x+6) = 3
Cross Multiplying we get:
2x+5x+10+4x+16 = 9x + 54
11x + 26 = 9x + 54
11x - 9x = 54 - 26
2x = 28
x = 14
thus the integers are 14 , 16, 18 , 20

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