Chapter 6, Problem 33SGR

To determine

To define the variables and to write the equations to find the number of each type of card Cristiano bought using the elimination method.

Answer to Problem 33SGR

System of equations to find the number of one type card and other type of card

  $x+y=24$

  $x+3y=50$

The number of cards bought of one type are 11 .

The number of cards bought of other type are 13.

Explanation of Solution

Given information: Given:

The cost of the card of one type is $ 1

The cost of the card of one type is $ 3

A total of 50 baseball cards were sold for the $ 50

Let

The number of cards bought of one type are x.

The number of cards bought of other type are y.

So according to the question:

The number of cards bought of one type + the number of cards bought of other type = 24

  $x+y=24$......Equation 1

Also according to the question:

The cost of one type card $\times$ number of one type cards sold + The cost of other type card $\times$ number of other type cards sold = 50

  $1\times x+3\times y=50$

  $\Rightarrow x+3y=50$ …..Equation 2

Subtracting Equation 2 from Equation 1:

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

Putting the value of y in Equation 1, we get:

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

So the number of cards bought of one type are 11 .

The number of cards bought of other type are 13.