Activity 1:  Puzzles with Currency Coins

Imagine you have coins of two denominations, say rupee 1 and rupee 2. You can select the number of coins, and see how equations can be formed, which is explained in the picture below. You can then write the equations on the board.

Using the tool shown in the picture, you can select the number of coins you have for by changing the number. As you change the number of coins you can see the equation that is formed with which you will know the total number of coins you have as well as the amount. You can save these equations by writing them on the board by clicking “Write to board” button. 

With this tool,

1. We can change the denominations, 
2. We can form the equations
3. We can write those equations on the board. 

Here is how it is done:
        Step 1:     Click on the two coins you want to select. 
        Step 2:     Select the number of each coin. The equation for the number coins you have selected is shown on the screen                          (see the figure below)
        Step 3:     Write the equation to the board.

Then the new equations for total value of these coins are shown.

You will also see that the equation will be different every time you change the number of coins you want to use. You can select the number of coins or  change their denomination.

We are now all set to create a puzzle, or a set of puzzles, with the information we have. Actually, we can create as many puzzles as we want from the same information. All that we have to do is to share some information with a friend and ask him (or her) to find the rest.

Here is a tool which will help us form linear equations for counts and total values of coins
 

Puzzle 1: I have a certain number of 1- and 2-rupee coins. Their total value is rupees 27. The value of 2-rupees coins is rupees16.
The puzzle is to find:
a) The number of 1 rupees coins,
b) The total number of coins I have

Puzzle 2: I have 12 coins of rupees 5 and 7 coins of rupees 10. What is the total value of the coins I have?

Puzzle 3: I have a few 2- and 10-rupees coins whose total value is rupees 100. The number of 2 rupees coins is 7. Here, the puzzle is to find out
a) How many 10-rupee coins I have?
b) What is the total value of the 2- rupees coins?

Give your answers in the comment box below. (Please mention the puzzle number along with your answer)