Chapter 9.9, Problem 2P

To determine

To calculate:

Number of stamps of each type did David buy.

Answer to Problem 2P

Number of stamps of each type did David buy is $1215\varphi ,2025\varphi ,645\varphi$ cent.

Explanation of Solution

Given information:

David paid $\$9.50$ for some $15\varphi ,25\varphi ,45\varphi$ .

Calculation:

Let,

  $x=$ the number of $15$ cent stamps.

  $y=$ the number of $25$ cent stamps

  $z=$ the number of $45$ cent stamps

It is given that total number of stamps is $38\varphi$

  $x+y+z=38\varphi$

Put the values,

  $\begin{array}{l}15x+25y+45z=9.50\\ y=2z+8\end{array}$

As Number of $25$ cent stamps is $8$ more than twice the number of $45$ cent stamps.

Three equations will be,

  $\begin{array}{l}x+y+z=38\\ 15x+25y+45z=950\\ 0x+y-2z=8\end{array}$

Now substitute the value of $y=2z+8$ ,

  $\begin{array}{l}x+2z+8+z=38\\ 15x+25\left(2z+8\right)+45z=950\end{array}$

Multiply equation by $-15$ ,

  $\begin{array}{l}-15x-45z=-450\\ 15x+95z=750\end{array}$

After adding these equations,

  $\begin{array}{l}50z=300\\ z=\frac{300}{50}\\ z=6\\ x+18=30\\ x=\frac{30}{18}\\ x=12\\ y=2\left(6\right)+8=20\end{array}$

Thus, Number of stamps of each type did David buy is $1215\varphi ,2025\varphi ,645\varphi$ cent.