pencils and jar?

Question

if i put 4 pencils into each jar i will have 1jar left over if i put 3 pencils into each jar i will have 1 pencil left over hoe many pencils and jars do i have?

Answer 1

let number of pencils = p
let number of jars = j

if i put 4 pencils into each jar i will have 1jar left over
therefore j-1 jars have 4 pencils in.
4 (j-1) = p

if i put 3 pencils into each jar i will have 1 pencil left over
j jars have three pencils plus 1 left over
3 j +1 = p

p = 3j+1 = 4(j-1)

3j+1 = 4j -4
1+4 = 4j-3j
j=5
p=3 j +1 =16

QED (quite easily done)