Joey decides to empty his piggy bank and his money. His bank is with only nickels and dimes. Joey counted a total of that up to $3.15. How many nickels and how many dimes does Joey have in his pi bank?

1 Answer
Mar 7, 2017

Potentially there are a number of solutions but I am just going to give you 1
3 nickels + 30 dimes #=$3.15#

Se the explanation for the algebraic represenation

Explanation:

Known:

Note that #-=# means 'equivalent to'

#1" dime "-= 10" cents"#
#1" nickel "-=5" cents"#
#$1 -= 100" cents"#

Let the count of dimes be #d#
Let the count of nickels be #n#

Standardizing everything into cents we have

#5n+10d=315#

Splitting the 315 into 300+15

10 will not divide exactly into 15 but 5 will

Set #5n=15#

#=>n=15/5=3" "color(red)("so we choose to have 3 nickels")#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Having 3 nickels leaves us 300 cents to deal with

Set #10d=300#

#=>d=300/10=30#

#color(red)("so we have 30 dimes to make up the difference")#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

There after you count nickels in pairs and make up the difference in dimes. Remember that we 'get rid' of the 15c by having #color(magenta)(3n=15) #. So the complete system is:

Using the count of #n# slightly differently coin count wise we have:

The 2n makes sure that we have an even number of nickels

#color(green)(color(magenta)(3)+2n+d="total coin count")#

Total count of nickels is 3+2n
Total count of dimes is d

Value wise we have:
#5(3+2n)+10d=315" cents"#