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.

Question

(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 gift certificate, we first need to set up the equation based on the information provided.

Let \( B \) represent the number of books Rachel can buy.

The cost of each book is $18.25, so the total cost for \( B \) books would be \( 18.25B \).

Since Rachel has a gift certificate for $75, we set up the equation as follows:

\[ 75 - 18.25B = 0 \]

Now, let's solve for \( B \):

1. Rearrange the equation: \[ 18.25B = 75 \]

2. Divide both sides by 18.25: \[ B = \frac{75}{18.25} \]

3. Calculate \( B \): \[ B \approx \frac{75}{18.25} \approx 4.1 \]

So, the rounded solution is approximately \( 4.1 \).

Since Rachel cannot buy a fraction of a book, she would round down to the nearest whole number to determine how many fully priced books she can afford.

Thus, she can buy \( 4 \) books.

Finally, we check if spending $75 is viable:

• The total cost for \( 4 \) books: \[ 4 \times 18.25 = 73 \]

Since \( 73 < 75 \), she is able to buy \( 4 \) books without exceeding her gift certificate amount, making this a viable solution.

In summary:

Equation: \( 75 - 18.25B = 0 \)
Solution: She can buy 4 books.
Is the value viable? Yes.

Answer 2

round 4 the the nearest tenth

Answer 3

Rounding \( 4 \) to the nearest tenth would still give you \( 4.0 \) since it is a whole number.

So if we follow your request:

Solution (rounded to the nearest tenth): She can buy 4.0 books.