To solve the problem, we need to create an equation that represents the situation and then solve it step-by-step.
(a) We need to formulate the equation based on the given information:
1. The cost of each book is [tex]$3.
2. Lucy receives a discount of $[/tex]6 off her total purchase.
3. After the discount, she spent [tex]$45.
Let \( b \) represent the number of books Lucy bought.
The total cost before the discount would be \( 3b \) because each book costs $[/tex]3 and she bought [tex]\( b \)[/tex] books. After applying the discount of [tex]$6, the total cost is reduced to $[/tex]45. Therefore, we can write the equation:
[tex]\[ 3b - 6 = 45 \][/tex]
(b) Now, let's solve the equation to find the number of books [tex]\( b \)[/tex].
1. Start with the equation:
[tex]\[ 3b - 6 = 45 \][/tex]
2. Add 6 to both sides of the equation to isolate the term with [tex]\( b \)[/tex] on one side:
[tex]\[ 3b - 6 + 6 = 45 + 6 \][/tex]
This simplifies to:
[tex]\[ 3b = 51 \][/tex]
3. Divide both sides of the equation by 3 to solve for [tex]\( b \)[/tex]:
[tex]\[ \frac{3b}{3} = \frac{51}{3} \][/tex]
This simplifies to:
[tex]\[ b = 17 \][/tex]
So, Lucy bought [tex]\( 17 \)[/tex] books.
