Question

How many different combination of Rs 5 and Rs 2 coins can be used to make a total of Rs 17? Order does not matter in this problem.

Answer 1

Answer:

5+5+5+2

=17

Step-by-step explanation:

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Answer 2

Given:

A total of Rs 17 is counted using only Rs 5 coins and Rs 2 coins.

To FInd:

The different combinations that are possible

Solution:

The given problem can be solved using the concepts of linear equations in 2 variables.

1. let the total number of 2 rupee coins be x and the total number of 5 rupee coins be y.

2. As the sum of the total number of 2 rupee coins and the total number of 5 rupee coins is 17. The equation can be written as,

=> 2x + 5y = 17

3. The possible solutions are:

=> The currency cannot be of decimal forms as it cannot be divided into parts. Hence, positive integral values which satisfy the equations of x and y are considered as combinations.

• If x = 1 then, 5y = 17 - 2 => y = 3.
• If x = 2 then y is 13/5 which is incorrect.
• If x = 3 then y is 11/5 which is incorrect.
• If x = 4 then y is 9/5 which is incorrect.
• if x = 5 then y is 7/5 which is incorrect.
• if x = 6 then, 5y = 17 - 12 => y = 1.
• if x = 7 then y is 3/5 which is not at all possible.    
• if x = 8 then y is 1/5 which is not possible as partly currency is not possible.

4. The only possible solutions are x = 1, y = 3 and x = 6, y = 1. Two different solutions are possible in this case.

Therefore, a total of 2 solutions are possible.