Let's break down the problem step-by-step to find the equation and determine the number of weeks it will take for Raymond to have only 24 books left.
Step 1: Define Variables
- Initial number of books: 120
- Number of books Raymond reads per week: 3
- Number of books Raymond wants to have left: 24
Step 2: Set Up the Equation
We need to find the number of weeks, [tex]\( w \)[/tex], it will take for Raymond to reduce the number of unread books from 120 to 24.
The number of books left unread after [tex]\( w \)[/tex] weeks is given by the initial number of books minus the number of books read per week times the number of weeks:
[tex]\[ \text{Books left} = 120 - 3w \][/tex]
We want this number to be equal to 24:
[tex]\[ 120 - 3w = 24 \][/tex]
Step 3: Solve for [tex]\( w \)[/tex]
Rearrange the equation to solve for [tex]\( w \)[/tex]:
[tex]\[ 120 - 3w = 24 \][/tex]
[tex]\[ 120 - 24 = 3w \][/tex]
[tex]\[ 96 = 3w \][/tex]
Divide both sides by 3:
[tex]\[ w = \frac{96}{3} \][/tex]
[tex]\[ w = 32 \][/tex]
So, the correct equation is [tex]\( 120 - 3w = 24 \)[/tex], and the number of weeks it will take is 32 weeks. Hence, the correct answer is:
A. [tex]\( 120 - 3w = 24 \)[/tex]; 32 weeks
