Chapter 6, Problem 33SGR

To determine

To calculate:

The solution set or number of cards bought by defining the variables and use elimination method.

Answer to Problem 33SGR

The number of bough cards are of $\$1$ per card is $11$ and of $\$3$ per card is $13$

Explanation of Solution

Given information:

One type cost $\$1$ per card.

The other cost $\$3$ per card.

Calculation:

Consider,

The number of one type card bought as $\$1$ per card: $x$

The number of other type card bought as $\$3$ per card: $y$

As per conditions of problem:

Bought $24$ baseball cards for $\$50$ :

  $x+y=24$.........(1)

  $x+3y=50$.........(2)

Take subtraction of both eqns.

  $\begin{array}{l}x+y-x-3y=24-50\\ -2y=-26\\ y=13\end{array}$

Calculate the value of $x$ by using the eq.(1):

  $\begin{array}{l}x+y=24\\ x+13=24\\ x=11\end{array}$

The solution set of the given system of equations is $\left(x,y\right)=\left(11,13\right)$

That means; $11$ cards that were $\$1$ and $13$ cards that were $\$3$ .