find three consecutive even integers

Question

find three consecutive even integers such that the sum of the first, twice the second, and three times the third is 124?

Answer 1

x, x+2, and x+4 are the integers

x+2(x+2)+3(x+4)=124

x+2x+4+3x+12=124

6x+16=124

6x=124-16

6x=108

x=108/6

x=18

x+2=20

x+4=22

 

Answer 2

here's what we know:

a + 2b + 3c = 124

a = b - 2

c = b + 2

 

b - 2 + 2b + 3(b + 2) = 124

b - 2 + 2b + 3b + 6 = 124

6b + 4 = 124

6b = 120

b = 20

 

a = 20 - 2 = 18

c = 20 + 2 = 22

 

check:

18 + 20 * 2 + 22 * 3 = 124

18 + 40 + 66 = 124

18 + 106 = 124

124 = 124