Bluee 發問於 科學及數學數學 · 1 十年前

# algebra

Three numbers are such that the second is the difference of three times the first and 6 while the third is the sum of 2 and 2/3 the second. The sum of the three numbers is 172. Find the largest number.

The yearly changes in the population of a city for three consecutive years are, respectively, 20% increase, 30% increase, and 20% decrease. What is the total percent change from the beginning to the end of the third year?

### 2 個解答

• 1 十年前
最愛解答

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 十年前

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.