To solve the problem of how many of each type of book Santiago bought, we'll need to set up a system of equations based on the information provided and the context in which we can categorize the books.
Step 1: Define Variables
Let:
- \( x \): the number of type A books
- \( y \): the number of type B books
Step 2: Set Up the Equations
From the problem statement, we know:
- The total number of books Santiago bought is 26, which can be expressed as: \[ x + y = 26 \]
Step 3: Additional Information Needed
To solve for \(x\) and \(y\), we need more information about the relationship between the two types of books (for example, the cost of each type, differences in numbers of each type, etc.). If we had more specifics, such as how many of one type he bought compared to the other, we could formulate a second equation.
For example:
- If he bought 10 more type A books than type B books, we would set up a second equation: \[ x = y + 10 \]
Step 4: Solve the System
Using the example equation:
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Substitute \( x \) in the first equation: \[ (y + 10) + y = 26 \] This simplifies to: \[ 2y + 10 = 26 \]
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Solve for \( y \): \[ 2y = 16 \implies y = 8 \]
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Now substitute back to find \( x \): \[ x = y + 10 = 8 + 10 = 18 \]
Step 5: Conclusion
Under the assumption that Santiago bought 10 more type A books than type B, he purchased:
- \( x = 18 \) (type A books)
- \( y = 8 \) (type B books)
Verification with Graph
To verify using a graph, you can plot the equation \( x + y = 26 \) on a graphing calculator, along with the additional constraints if you have them. The intersection points will help you visually confirm the solution.
If there is any other specific relationship or additional equations you have regarding the types of books, please provide that so we can refine the calculations accordingly!
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