Find two numbers such that if 18 is added to the first number it becomes twice the second number and if 16 is added to the second number it becomes three times the first number.

10 and 14

Step-by-step explanation:

Let the first number be x and the second number be y, then

x + 18 = 2y → (1)

y + 16 = 3x → (2)

Rearrange (1) expressing x in terms of y by subtracting 18 from both sides

x = 2y - 18 → (3)

Substitute x = 2y - 18 into (2)

y + 16 = 3(2y - 18) ← distribute

y + 16 = 6y - 54 ( subtract 6y from both sides )

- 5y + 16 = - 54 ( subtract 16 from both sides )

- 5y = - 70 ( divide both sides by - 5 )

y = 14

Substitute y = 14 into (3) for corresponding value of x

x = (2 × 14) - 18 = 28 - 18 = 10

The 2 numbers are 10 and 14

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.