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We are given the equation $5b + 2r = 12$, where:
- $b$ is the pounds of beans (costing $5 per pound),
- $r$ is the pounds of rice (costing $2 per pound),
- The total budget is $12.

We need to complete the table based on this equation:

### 1. First row ($b = 2$):
Substitute $b = 2$ into the equation:
\[
5(2) + 2r = 12 \implies 10 + 2r = 12 \implies 2r = 2 \implies r = 1
\]
This matches the table (already filled).

### 2. Second row ($r = 4.5$):
Substitute $r = 4.5$ into the equation:
\[
5b + 2(4.5) = 12 \implies 5b + 9 = 12 \implies 5b = 3 \implies b = 0.6
\]
This is also correct.

### 3. Third row ($b = b$):
This requires us to solve for $r$ in terms of $b$:
\[
5b + 2r = 12 \implies 2r = 12 - 5b \implies r = \frac{12 - 5b}{2}
\]
Thus, for any given $b$, the value of $r$ is $r = \frac{12 - 5b}{2}$.

Would you like to substitute any specific values for $b$ to complete the table, or is there anything you want more details on?

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Here are 5 related questions to explore further:
1. What happens to the value of $r$ if you increase $b$ beyond 2 pounds?
2. How much rice can Abdel buy if he buys no beans at all?
3. If Abdel decides to spend all $12 on beans, how many pounds can he purchase?
4. How would the equation change if the price of beans increased to $6 per pound?
5. Can you graph the relationship between $b$ and $r$ using the equation $5b + 2r = 12$?

**Tip:** When solving systems of equations like this, try isolating one variable to simplify the calculations.

Abdel wants to spend $12 on beans and rice. Beans cost $5 per pound, and rice costs $2 per pound. Complete the table based on the equation 5b + 2r = 12.

Learn how to solve the linear equation 5b + 2r = 12, where b represents pounds of beans and r represents pounds of rice. Follow a step-by-step process to complete a table based on this equation. Suitable for students in Grades 6-8.

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