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

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet