Chapter 5.5, Problem 27P

You have only nickels and dimes in your piggy bank. When you ran the coins through a change counter, it indicated you have 595 cents. Write and graph an equation that represents this situation. What are three combinations of nickels and dimes you could have?

To determine

Tograph: The combinations of nickels and dimes.

Explanation of Solution

Given information:

Total money =595 cents

Nickels = 5 cents.

Dimes = 10 cents.

Calculation:

According to the question, the equation will be

  $5n+10d=595$

(Multiply nickels by any numberthen solve the equation to find the dimes.)

(i) let $n=5$

  $\begin{array}{l}5\left(5\right)+10d=595\\ 25+10d=595\\ 10d=595-25\\ 10d=570\\ d=57\end{array}$

5 nickels and 57 dimes.

(ii) let $n=10$

  $\begin{array}{l}5\left(10\right)+10d=595\\ 50+10d=595\\ 10d=595-50\\ 10d=550\\ d=55\end{array}$

10 nickels and 55 dimes.

(iii) let $n=15$

  $\begin{array}{l}5\left(15\right)+10d=595\\ 75+10d=595\\ 10d=595-75\\ 10d=520\\ d=52\end{array}$

15nickels and 52 dimes.

Graph:

Now, graph for numbers of nickels and dimes will be -

  

Interpretation: When the number of nickels increase the number of dimes decreases.