Question

Rachel was given a gift certificate for her birthday for $75. She decides to purchase new books. Each book that she purchases costs $18.25. Write an equation to determine how many books she can buy and spend exactly the $75. Then solve it and determine if the value is a viable solution. (1 point) Equation: - B = 0 Solution: She can buy books (round to the nearest tenth). Is the value viable?

Answer 1

To determine how many books Rachel can buy with her $75 gift certificate, we can set up the following equation:

Let \( B \) be the number of books she can buy. The total cost of the books can be represented by the equation:

\[
18.25B = 75
\]

Now, we'll solve for \( B \):

\[
B = \frac{75}{18.25}
\]

Calculating the value:

\[
B \approx \frac{75}{18.25} \approx 4.115
\]

Now, rounding to the nearest tenth, \( B \) is approximately 4.1.

Next, we need to determine if this is a viable solution in terms of purchasing whole books. Since Rachel cannot buy a fraction of a book, we check the whole number values below and above our solution:

1. **If \( B = 4 \)**:
\[
\text{Total cost} = 18.25 \times 4 = 73
\]
This is under $75 and is a feasible option.

2. **If \( B = 5 \)**:
\[
\text{Total cost} = 18.25 \times 5 = 91.25
\]
This exceeds $75 and is not a feasible option.

Thus, the only viable solution for how many whole books Rachel can buy is 4 books, which costs her $73, leaving her with a remainder of \$2 from her $75 gift certificate.

In conclusion:
- **Equation**: \( 18.25B = 75 \)
- **Solution**: Rachel can buy 4 books.
- **Is the value viable?**: Yes, buying 4 books is a valid solution.