Jane bought some books for $5 each and received a discount of $7 off of her total purchase. She spent $58 after the discount. How many books did she buy? Write an equation that cou... Jane bought some books for $5 each and received a discount of $7 off of her total purchase. She spent $58 after the discount. How many books did she buy? Write an equation that could be used to answer the question above. First, choose the appropriate form. Then, fill in the blanks with the numbers 5, 7, and 58. Let b represent the number of books. Solve the equation in part (a) to find the number of books.
Understand the Problem
The question is an algebra problem that requires to write an equation representing a scenario where Jane bought books, received a discount, and spent an amount. You must choose the correct equation form and solve for the number of books.
Answer
(a) $5b - 7 = 58$ (b) $b = 13$
Answer for screen readers
(a) $5b - 7 = 58$ (b) $b = 13$
Steps to Solve
- Determine the correct equation form
Since Jane received a discount, the equation should subtract the discount from the total cost of the books before the discount. The cost of the books before the discount is $5 \cdot b$, where $b$ is the number of books. The discount is $7. The final price after the discount is $58. Therefore, the equation form will be $ _b - _ = _ $.
- Fill in the blanks with the provided numbers
Given that the cost per book is $5, the discount is $7, and the final cost is $58, the equation becomes: $5b - 7 = 58$
- Solve the equation for b
To solve for $b$, add 7 to both sides of the equation: $5b - 7 + 7 = 58 + 7$ $5b = 65$
- Isolate b
Divide both sides by 5 to isolate $b$: $\frac{5b}{5} = \frac{65}{5}$ $b = 13$
(a) $5b - 7 = 58$ (b) $b = 13$
More Information
The answer indicates that Jane bought 13 books. At $5 each, the books cost $65 in total. After a discount of $7, she paid $58.
Tips
A common mistake would be choosing the addition equation instead of the subtraction equation, or misplacing the numbers within the equation. For example, someone might write $5b + 7 = 58$ or $7b - 5 = 58$. Another common mistake could be to add 5 to both sides instead of multiplying.
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