Math Problem Statement

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?

Solution

Let's analyze and solve the problem provided in the image step by step.

Problem Statement

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

We are asked to choose the correct system of equations and solve how much Jorge and Lester saved individually.

Defining Variables

  • Let jj represent the amount Jorge saved.
  • Let ll represent the amount Lester saved.

Information from the Problem

  1. The total amount saved by both Jorge and Lester is 6060. Therefore: j+l=60j + l = 60
  2. Jorge saved $9 more than twice the amount Lester saved, meaning: j=2l+9j = 2l + 9

Choosing the Correct System of Equations

We now check which option matches the equations we derived:

  • The first equation is j+l=60j + l = 60.
  • The second equation is j=2l+9j = 2l + 9.

From the options in the image, Option B matches this system of equations:

\begin{cases} j + l = 60 \\ j = 2l + 9 \end{cases}$$ --- ### Solving the System of Equations We have the system: $$\begin{cases} j + l = 60 \\ j = 2l + 9 \end{cases}$$ 1. **Substitute** $$j = 2l + 9$$ into the first equation: $$(2l + 9) + l = 60$$ 2. **Simplify** and solve for $$l$$: $$2l + 9 + l = 60 \\ 3l + 9 = 60 \\ 3l = 60 - 9 \\ 3l = 51 \\ l = \frac{51}{3} \\ l = 17$$ So, Lester saved **$17**. 3. **Substitute** $$l = 17$$ into the second equation to find $$j$$: $$j = 2(17) + 9 = 34 + 9 = 43$$ So, Jorge saved **$43**. --- ### Final Answer: - **Jorge saved**: $43 - **Lester saved**: $17 Would you like further explanation or details on any of the steps? ### Follow-up Questions: 1. What other methods could be used to solve systems of equations? 2. How would the problem change if Jorge had saved $9 *less* than twice Lester's amount? 3. What is the significance of substitution in solving systems of equations? 4. Can you graph these equations and find the solution visually? 5. How do systems of equations apply in real-world financial scenarios? ### Tip: Always verify your solution by substituting the values back into the original equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Equations
Substitution

Formulas

j + l = 60
j = 2l + 9

Theorems

Substitution Method

Suitable Grade Level

Grades 6-8

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