have some pencils and some jars. If I put 4 pencils into each jar I will have one jar left over If I put 3 pencils into each jar I will have one pencil left over How many pencils and how many jars?

Let j = number of jars, p = number of pencils. If 4 pencils per jar leaves 1 jar empty: p = 4(j-1). If 3 pencils per jar leaves 1 pencil: p = 3j + 1. Equating: 4j - 4 = 3j + 1, so j = 5. Then p = 3(5) + 1 = 16. Checking: 16 pencils with 4 per jar uses 4 jars (1 empty), and 16 pencils with 3 per jar uses 5 jars with 1 left over.