if J=the number of Julius's pencils and L=the number of Lucy's pencils, then 2J=L

Question

There are twice as many pencils in Julius's pencil box than in Lucy's. Julius attempts to write this relationship as an equation which he believes is correct. He writes: if J=the number of Julius's pencils and L=the number of Lucy's pencils, then 2J=L. How would you convince Julius that his equation is incorrect?

Answer 1

The proof lies in the total number of pencils in both julius's and lucy's boxes. Assuming the above is correct then,

 

2J + L = T,  where T is total number of pencils

 

if we substitute 2J = L into the equation we get L+L = T, 2L = T, L = T/2 

 

based on the above the number of Lucy's pencils is half the total number of pencils

 

substitute L=T/2  into the 2nd equation you get  2J  + (T/2) = T , 2J = T - T/2, 2J = T/2 = L , and 2J = L

 

Therefore Julius equation L = 2J or 2J = L is correct