Jorge and Lester are saving money. Together they have saved $60
. Jorge saved $9
more than twice the amount Lester saved.

Which system of equations can be used to determine the amount Jorge saved, j
, and the amount Lester saved, l
?
A.
j + l = 60
j = 2l + 9

B.
j ‒ l = 60
j = 2l + 9

C.
j ‒ l = 9
j = 2l + 60

D.
j + l = 60
j = 2l ‒ 9

5b.
How much did Jorge and Lester save individually?

Jorge saved $$ dollars and Lester saved $$ dollars.
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To determine the system of equations that can be used to find how much Jorge and Lester saved, let's break down the information:

1. **Together, they saved $60**, which gives us the equation:  
   \[
   j + l = 60
   \]
   where $ j $ is the amount Jorge saved, and $ l $ is the amount Lester saved.

2. **Jorge saved $9 more than twice the amount Lester saved**, which translates to the equation:  
   \[
   j = 2l + 9
   \]
   This means Jorge's savings are $9 more than double Lester's savings.

### Now, let's match this to the choices provided:

- **Choice A**:  
  \[
  j + l = 60 \quad \text{and} \quad j = 2l + 9
  \]  
  This is correct because it accurately represents both pieces of information given in the problem.

- **Choice B**:  
  \[
  j - l = 60 \quad \text{and} \quad j = 2l + 9
  \]  
  This is incorrect because the first equation should represent their total savings, not the difference.

- **Choice C**:  
  \[
  j - l = 9 \quad \text{and} \quad j = 2l + 60
  \]  
  This is incorrect because both equations are wrong. The first equation should show total savings, and the second doesn't match the relationship between Jorge and Lester's savings.

- **Choice D**:  
  \[
  j + l = 60 \quad \text{and} \quad j = 2l - 9
  \]  
  This is incorrect because the second equation doesn't reflect the correct relationship (Jorge saved **$9 more**, not $9 less).

### The correct system of equations is:
\[
\boxed{A}
\]

### 5b. How much did Jorge and Lester save individually?

To find out how much they saved, solve the system:

1. From the first equation $ j + l = 60 $, we know:
   \[
   j = 60 - l
   \]

2. Substitute this into the second equation $ j = 2l + 9 $:
   \[
   60 - l = 2l + 9
   \]

3. Solve for $ l $:
   \[
   60 - 9 = 2l + l
   \]
   \[
   51 = 3l
   \]
   \[
   l = \frac{51}{3} = 17
   \]

4. Now, substitute $ l = 17 $ into $ j = 60 - l $:
   \[
   j = 60 - 17 = 43
   \]

Thus, **Jorge saved $43**, and **Lester saved $17**.

---

### Final Answer:
- Jorge saved **$43**.
- Lester saved **$17**.

---

Would you like more details or have any questions about the solution?

### Here are 5 questions for further exploration:

1. What would happen if Jorge saved $5 more than twice Lester's savings?
2. If they together saved $100 instead of $60, how would the equations change?
3. What if Jorge saved half of what Lester saved? What system of equations would that create?
4. How can you solve this system of equations graphically?
5. What are the advantages of using substitution vs. elimination in solving this problem?

### Tip:
When dealing with word problems, always translate the relationships given in the problem directly into mathematical equations to avoid confusion.

Jorge and Lester are saving money. Together they have saved $60. Jorge saved $9 more than twice the amount Lester saved. Which system of equations can be used to determine the amount Jorge saved, j, and the amount Lester saved, l? How much did Jorge and Lester save individually?

Learn how to solve a system of equations to determine how much Jorge and Lester saved. Jorge saved $9 more than twice what Lester saved, and together they saved $60. This detailed step-by-step solution explains how to use substitution to find the individual amounts. Suitable for students in Grades 6-8.

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