Math Problem Statement

S bought 4 pens and 3 books. Each pen costs half of one book. The total cost of the items is $8. What is the cost for one pen?

Solution

Let the cost of one book be denoted as xx, and since each pen costs half of a book, the cost of one pen is x2\frac{x}{2}.

Given that S bought 4 pens and 3 books, we can set up the total cost equation:

4×x2+3x=84 \times \frac{x}{2} + 3x = 8

Simplifying the first term:

2x+3x=82x + 3x = 8

Now combine like terms:

5x=85x = 8

Solve for xx:

x=85=1.6x = \frac{8}{5} = 1.6

Now that we know the cost of one book is 1.61.6 dollars, the cost of one pen is:

x2=1.62=0.8\frac{x}{2} = \frac{1.6}{2} = 0.8

Thus, the cost of one pen is $0.80.

Would you like further details or have any questions?

Here are some related questions to extend your understanding:

  1. What would be the total cost if S bought 5 pens and 4 books?
  2. If each pen cost $0.80, how many pens can S buy with $12?
  3. What is the total cost if S bought 6 pens and 2 books?
  4. If the cost of each pen increased by 20%, what would the new cost be?
  5. How would the total cost change if S received a 10% discount on the books?

Tip: When solving word problems, assigning variables to unknown quantities and translating conditions into equations helps simplify the process.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Total cost equation: 4 * (cost of pen) + 3 * (cost of book) = 8
Pen cost: (cost of book) / 2

Theorems

Basic algebraic manipulation and solving linear equations

Suitable Grade Level

Grades 6-8