problem solving?!

Question

Sarah has 26 coins. Some are pennies and some are nickels. If the coins are worth 62 cents, how many are nickels?

Answer 1

Hi Brenda,

This problem can be handled using algebraic equations or by a 'guess-and-check' approach.  If you guess there are 10 nickels, then there are 16 pennies.  When you 'check' the numbers, the value of the nickels would be 50 cents and the value of the pennies would be 16 cents, for a total of 66 cents.  Since 66 cents is a little too high, you can decrease the number of nickels to 9 nickels and increase the number of pennies to 17.  The value of the nickels would be 45 cents and the value of the pennies would be 17 cents.  Since that total matches the problem, the answer is 9 nickels and 17 pennies.

I hope you enjoy the challenge that math provides!

Mary Ann

Answer 2

Let's start with what we know:

Number of coins:

n + p = 26

number of cents:

5n + p = 62

 

We can use the elimination method here by multiplying the first equation by -1:

5n + p = 62

-n - p = -26

4n = 36

Isolate n by dividing by 4:

n = 9

 

Now that we know the number of nickels, we can find our pennies:

9 + p = 26

p = 17

 

Now to check our answer:

5 * 9 + 17 = 62

45 + 17 = 62

62 = 62