Let's solve this step by step.
---
Step 1: Define variables
Let:
- $ w $ = number of weeks
Let:
- $ T(w) $ = number of books in Tammy's library after $ w $ weeks
- $ L(w) $ = number of books in Lyla's library after $ w $ weeks
---
Step 2: Write equations based on the situation
Tammy's library:
- Starts with 14 books
- Adds 3 books per week
- So:
$$
T(w) = 14 + 3w
$$
Lyla's library:
- Starts with 18 books
- Adds 1 book per week
- So:
$$
L(w) = 18 + 1w
$$
---
Step 3: Set up the system of equations
We want to find when the two libraries have the same number of books:
$$
14 + 3w = 18 + w
$$
---
Step 4: Solve using substitution (or algebraically)
We already have one equation with one variable, so we can solve directly.
$$
14 + 3w = 18 + w
$$
Subtract $ w $ from both sides:
$$
14 + 2w = 18
$$
Subtract 14 from both sides:
$$
2w = 4
$$
Divide by 2:
$$
w = 2
$$
---
Step 5: Find the number of books at that time
Plug $ w = 2 $ into either equation.
Using Tammy’s:
$$
T(2) = 14 + 3(2) = 14 + 6 = 20
$$
Using Lyla’s:
$$
L(2) = 18 + 1(2) = 18 + 2 = 20
$$
✔ Both have 20 books after 2 weeks.
---
✔ Final Answer:
After
2 weeks, the two teachers' libraries will each have
20 books.
---
Answer in blanks:
After
2 weeks, the two teachers' libraries will each have
20 books.
Parent Tip: Review the logic above to help your child master the concept of substitution word problems worksheet.
