Chapter 3.4, Problem 2ST

To determine

To find: All possibilities for the number of each type of record that she bought.

Answer to Problem 2ST

Toni might have bought $1$ jazz and $7$ classical records or $4$ jazz and $5$ classical records or $7$ jazz and $3$ classical records or $10$ jazz and $1$ classical record.

Explanation of Solution

Given information: Jazz records cost $\$4$ each, classical records cost $\$6$ each, total amount spent was $\$46$ .

Calculation:

Let the number of jazz records bought by Toni be $x$ and the number of classical records bought by Toni be $y$ ,

Formulating an equation as per given situation,

  $4x+6y=46$

Putting different values of $x$ in equation to find $y$ ,

  $\begin{array}{lllllllllll}x\hfill & 1\hfill & 2\hfill & 3\hfill & 4\hfill & 5\hfill & 6\hfill & 7\hfill & 8\hfill & 9\hfill & 10\hfill \\ y\hfill & 7\hfill & \frac{19}{3}\hfill & \frac{17}{3}\hfill & 5\hfill & \frac{13}{3}\hfill & \frac{11}{3}\hfill & 3\hfill & \frac{7}{3}\hfill & \frac{5}{3}\hfill & 1\hfill \end{array}$

As after $x=10,$ value of $y$ will definitely become less than $1$ , which is not desirable, so not calculating further values,

From table picking up the values in which $y$ is a positive integer, points are,

  $\{(1,7),(4,5),(7,3),(10,1)\}$

Thus, Toni might have bought $1$ jazz and $7$ classical records or $4$ jazz and $5$ classical records or $7$ jazz and $3$ classical records or $10$ jazz and $1$ classical record.