The sum of three numbers is 14. The largest number is 4 times the smallest number. The sum of the smallest and twice the largest is 18. What are all three numbers?

a = 2, b = 4, c = 8

Step-by-step explanation:

Let:

First (smallest) number = a

Second number = b

Third number(Largest) = c

The sum of three numbers is 14.

a + b + c = 14 Equation 1

The largest number is 4 times the smallest number.

c = 4a Equation 2

The sum of the smallest and twice the largest is 18.

a + 2c = 18 Equation 3

We substitute Equation 2 in Equation 3

to solve for a

a + 2(4a) = 18

a + 8a = 18

9a = 18

a = 18/9

a = 2

Hence, the smallest number = 2

We find c

c = 4a Equation 2

c = 4(2)

c = 8

The largest number is 8

We find b

a + b + c = 14 Equation 1

2 + b + 8 = 14

b + 10 = 14

b = 14 - 10

b = 4

What are all three numbers?

a = 2, b = 4, c = 8