algebra

Let the first number be x,
then the second number = 3x-6
and the thrid number = 2+ 2/3 * (3x-6)

As the sum of the three numbers is 172,
so, x + (3x-6) + [2+ 2/3 * (3x-6)] = 172
4x-6 + (2 + 2x - 4) = 172
6x - 8 = 172
x = 60

so the first, second and third number are respectively = 60, 174, and 118

so, the largest number = 174

Let population in the beginning = y
then population at the end of the third year
= y * (1+20%) * (1+30%) * (1-20%)
= 1.2 * 1.3 * 0.8y
= 1.248 y

so, the total percent change from the beginning to the end of the third year
= (1.248y - y)/y * 100%
= 0.248 * 100%
= 24.8% (increase)

1)Let the 3 number as x ,y ,z

y = 3x -6
z = 2 + 2/3(y) = 2 + 2/3(3x-6) = 2x -2

x + y + z = 172
x + 3x - 6 + 2x - 2 = 172
6x - 8 = 172
6x = 180
x = 30

therefore: x = 30, y = 84, z = 58 ( Proof: 30 + 84 + 58 = 172)
y is the largest...84

2) let the original population as P
Population at the end of 3rd year:
(1 + 20%) * (1 + 30%) * (1 - 20%) * P
= 1.2 * 1.3 * 0.8 * P
= 1.248P

the percent change in 3 consecutive years:
(1.248P - P) / P
= (1.248 - 1)P / P
= 0.248
= 24.8 %

therefore, the city has a 24.8% population growth from the beginning to the end of the third year.