Question

The sum of three numbers is 21. The second number is two more than twice the first number. The second number is three times the third number. What are the numbers?

Answer 1

The numbers are:

5, 12 and 4

Explanation:

a + b + c = 21 Eq. 1

b = 2a +2 Eq. 2

b = 3c Eq. 3

From Eq. 2:

b - 2 = 2a

(b-2)/2 = a Eq. 4

From Eq. 3:

c = b/3 Eq. 5

Replacing Eq. 4 and Eq. 5 in Eq. 1:

(b-2)/2 + b + b/3 = 21

3(b-2)/6 + 6b/6 + 2b/6 = 126/6

3(b-2) + 6b + 2b = 126

(3*b + 3*-2) + 8b = 126

3b - 6 + 8b = 126

11b = 126 + 6

11b = 132

b = 132/11

b = 12

from Eq. 4

(b-2)/2 = a

(12-2)/2 = a

10/2 = a

a = 5

from Eq. 5

c = b/3

c = 12/3

c = 4

Check:

from Eq. 1

a + b + c = 21

5 + 12 + 4 = 21