Question

afia makes a line using 19 pencils of equal length. orlando makes line using 21 pencils of equal length. Afia's line is 33 cm longer than Orlando's line. what length pencil did each use​

Answer 1

Given : afia makes a line using 19 pencils of equal length. orlando makes line using 21 pencils of equal length. Afia's line is 33 cm longer than Orlando's line.

To find : what length pencil did each use​

Solution:

Let say  afia pencil length  = A  cm

He uses 19 pencils

so Total length of afia = 19A  cm

Let say orlando pencil length = B   cm

He used 21 pencils

so Total length of Orlando = 21B  cm

19 A   - 21 B   =  33  

Let say A = B + x

=> 19 (B + x) - 21B  = 33

=> 19B  + 19x  - 21B = 33

=> 19x  = 33  + 2B  

=> 19(x - 1) = 14 + 2B  

14 + 2B   must be  a multiple of 19

B = 12  => 14 + 24 = 38

=> x - 1 = 2

=> x = 3

B = 12  , A = 15

19 * 15 = 285 cm

21 * 12  = 252  cm

285 - 252 = 33 cm

So Length of pencils  are    15 cm & 12 cm

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