Orion buys 3 books for a total of
8 plus sales tax for each book. He wants to know how much the sales tax is for one book. Which quantity is unknown? the sales tax for each book Let t equal the sales tax Orion pays for each book. Write an equation that represents the situation.
The Correct Answer and Explanation is:
✅ Correct Equation:
Let tt be the sales tax for each book.
Orion pays $8 plus sales tax per book, so the total cost per book is 8+t8 + t.
He buys 3 books, and the total cost is $25.50.
So the equation is: 3(8+t)=25.503(8 + t) = 25.50
📝 Explanatio
This problem involves setting up an equation to find an unknown value using the information provided. Let’s break it down step-by-step.
We are told that Orion buys 3 books for a total of $25.50. For each book, he pays $8 plus sales tax. The goal is to find out how much the sales tax per book is, which is the unknown quantity.
We define this unknown value with a variable:
Let tt represent the sales tax per book.
The total price for one book is then: 8+t8 + t
This represents the base price of $8, plus the additional unknown tax tt.
Since Orion bought 3 books, the total amount he paid is the cost of one book multiplied by 3: 3×(8+t)3 \times (8 + t)
We are told that this total is equal to $25.50, so we write the equation: 3(8+t)=25.503(8 + t) = 25.50
This is a linear equation with one variable, and it models the situation perfectly. From here, we can solve the equation by distributing and isolating tt: 3(8+t)=25.50⇒24+3t=25.50⇒3t=1.50⇒t=0.503(8 + t) = 25.50 \Rightarrow 24 + 3t = 25.50 \Rightarrow 3t = 1.50 \Rightarrow t = 0.50
So, the sales tax per book is $0.50.
This problem demonstrates how to use algebra to model a real-world scenario by translating words into mathematical expressions and solving for an unknown.
