Question

The total length of pencils A, B and C is 29 cm. Pencil a is 11 cm shorter then pencil B, and pencil B is twice as long a pencil C. How long is pencil A?

Answer 1

The length of pencil A is 5 cm

Solution:

Let the length of pencil A be "x"

Let the length of pencil B be "y"

Let the length of pencil C be "z"

The total length of pencils A, B and C is 29 cm

Therefore,

length of pencil A + length of pencil B + length of pencil C = 29

x + y + z = 29 ------------ eqn 1

Pencil A is 11 cm shorter then pencil B

x = y - 11 ------- eqn 2

Pencil B is twice as long a pencil C

y = 2z

`z = (y)/(2)` ------ eqn 3

Substitute eqn 2 and eqn 3 in eqn 1

`y - 11 + y + (y)/(2) = 29\\\\2y + (y)/(2) = 29 + 11\\\\(4y+y)/(2) = 40\\\\5y = 80\\\\y = 16`

Substitute y = 16 in eqn 2

x = 16 - 11

x = 5

Thus length of pencil A is 5 cm