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?

Question

asked Mar 3, 2021 303 views

1 Answer

Tmarwen · Answer 1 · 2021-03-09T20:12:16+0000

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