Chapter 0, Problem 1PR

To determine

Number of postcards and number of letters sent by the person D to his friends.

Answer to Problem 1PR

5 postcards and 5 letters

Explanation of Solution

Given:

Price of stamps for each postcard is $0.26

Price of stamps for each letter is $0.41

Total money available for stamps to the person D is $3.35

Calculation:

Let us solve this question using a system of equations.

Let the number of Postcards sent by the person D be x and the number of letters sent by the person D be y.

As we know, the person D sent postcards and letters to a total of 10 friends.

Therefore, $x+y=10\left(1\right)$

Price of stamps for each postcard is $0.26 and price of stamps for each letter is $0.41

Total money available for stamps to the person D is $3.35.

Therefore,

  $0.26x+0.41y=3.35\left(2\right)$

Now, we will solve the two equations to determine the value of x and y

First, multiply equation (1) with 0.26

  $0.26x+0.26y=2.60\left(3\right)$

Now, subtract equation (3) from equation (2)

  $\begin{array}{c}\left(0.26-0.26\right)x+\left(0.51-0.26\right)y=3.35-2.60\\ 0x+0.15y=0.75\\ y=5\end{array}$

Now put the value of y in equation (1) to determine value of x

  $\begin{array}{c}x+5=10\\ x=5\end{array}$

Therefore, the person D sent 5 postcards and 5 letters to his friends.