Can You Solve These Tricky Pencils and Jars Puzzles Using Algebra? Let's Discuss!

Pencils and Jars Puzzles

Puzzle 1:

I 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?

Puzzle 2:

Again, I have some pencils and some jars. If I put 9 pencils into each jar, I will have two jars left over. If I put 6 pencils into each jar, I will have three pencils left over. How many pencils and how many jars?

Stuck? The first one is quite easy. The second question is more involved. You will probably need to create an algebraic expression for each statement in the problem. Solve the equations, and you have your answer.

Jitendra Patel

To solve the first puzzle, let's denote the number of pencils as 'p' and the number of jars as 'j'. From the given conditions, we can create the following equations:
1. 4j + 1 = p
2. 3j + 1 = p
By solving these equations simultaneously, we find that there are 13 pencils and 3 jars.

For the second puzzle, we can similarly denote the number of pencils as 'p' and the number of jars as 'j'. The equations are:
1. 9j + 2 = p
2. 6j + 3 = p
Solving these equations, we get the solution of 29 pencils and 4 jars.

Remember to always create algebraic expressions for each statement in the problem to effectively solve such puzzles.