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The given image shows a word problem that involves a chef buying ribs and chicken. The total cost is represented by the equation:

\[
0.9c + 1.89r = 17.01
\]

where $c$ represents the pounds of chicken, and $r$ represents the pounds of ribs. The equation is derived from the prices of chicken ($0.90 per pound) and ribs ($1.89 per pound), totaling $17.01.

The task asks to check whether two provided equations are equivalent to this equation:

1. **$ c = 18.9 - 2.1r $** (marked "yes" in the image)
2. **$ r = \frac{-10}{21}c + 9 $** (marked "no" in the image)

Finally, the explanation discusses why solving the equation for $ r $ might be useful in certain situations and suggests that finding an equivalent equation could make it easier to solve for one variable when the other is known.

### Verification of the given equations:

1. **First equation**: $ c = 18.9 - 2.1r $
   - Start from the original equation:
     \[
     0.9c + 1.89r = 17.01
     \]
   - Solving for $ c $:
     \[
     0.9c = 17.01 - 1.89r
     \]
     \[
     c = \frac{17.01 - 1.89r}{0.9}
     \]
     Simplifying:
     \[
     c = 18.9 - 2.1r
     \]
   - This confirms the first equation is equivalent to the original, which is correctly marked "yes."

2. **Second equation**: $ r = \frac{-10}{21}c + 9 $
   - Solving the original equation for $ r $:
     \[
     0.9c + 1.89r = 17.01
     \]
     Rearranging:
     \[
     1.89r = 17.01 - 0.9c
     \]
     \[
     r = \frac{17.01 - 0.9c}{1.89}
     \]
     Simplifying:
     \[
     r = 9 - \frac{10}{21}c
     \]
   - This is equivalent to $ r = -\frac{10}{21}c + 9 $, which matches the form of the second equation but is marked "no" in the image. The marking appears to be a mistake.

### Why might it be helpful to solve for $ r $?
Solving the equation for $ r $ (ribs) could be helpful because it would allow you to quickly find how many pounds of ribs are bought when the pounds of chicken are known.

Would you like further clarification or more details on any part of this? Here are five related questions:

1. Can you explain the steps for isolating $ r $ in more detail?
2. What is the practical significance of solving for $ c $ versus $ r $?
3. How can you verify the correctness of an equivalent equation?
4. Why is the solution $ r = \frac{-10}{21}c + 9 $ still correct even though marked "no"?
5. How does simplifying an equation help in real-life problem solving?

**Tip**: When working with linear equations, try to isolate variables step by step, checking each stage for accuracy.

A chef bought $17.01 worth of ribs and chicken. Ribs cost 1.89 per pound and chicken costs 0.90 per pound. The equation 0.9c + 1.89r = 17.01 represents the relationship between the quantities in this situation. Determine whether each of the following equations is equivalent to 0.9c + 1.89r = 17.01.

Learn how to solve the linear equation representing a chef's purchase of $17.01 worth of ribs and chicken. This algebra problem covers the costs per pound of ribs and chicken and determining equivalent equations for finding how much of each item was purchased. Suitable for students in Grades 8-10.

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