# 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 $\equiv$ means 'equivalent to'

$1 \text{ dime "-= 10" cents}$
$1 \text{ nickel "-=5" cents}$
$1 -= 100" cents" Let the count of dimes be $d$Let the count of nickels be $n$Standardizing everything into cents we have $5 n + 10 d = 315$Splitting the 315 into 300+15 10 will not divide exactly into 15 but 5 will Set $5 n = 15$=>n=15/5=3" "color(red)("so we choose to have 3 nickels") ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Having 3 nickels leaves us 300 cents to deal with Set $10 d = 300$$\implies d = \frac{300}{10} = 30$$\textcolor{red}{\text{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 $\textcolor{m a \ge n t a}{3 n = 15}$. 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 $\textcolor{g r e e n}{\textcolor{m a \ge n t a}{3} + 2 n + d = \text{total coin count}}$Total count of nickels is 3+2n Total count of dimes is d Value wise we have: $5 \left(3 + 2 n\right) + 10 d = 315 \text{ cents}\$