https://file.aiquickdraw.com/mathbot/file/1729538074384n1i2035a.jpg

The system of equations provided in the image is:

\[
c + 2d = 4.90
\]
\[
2c + 3d = 8.60
\]

where:
- $c$ is the cost of one cup of coffee,
- $d$ is the cost of one doughnut.

We need to solve this system to find the cost of one cup of coffee, $c$.

### Step 1: Solve one equation for one variable
Let's solve the first equation $c + 2d = 4.90$ for $c$:

\[
c = 4.90 - 2d
\]

### Step 2: Substitute into the second equation
Substitute $c = 4.90 - 2d$ into the second equation $2c + 3d = 8.60$:

\[
2(4.90 - 2d) + 3d = 8.60
\]

### Step 3: Simplify the equation
Expand and simplify:

\[
2 \times 4.90 - 2 \times 2d + 3d = 8.60
\]
\[
9.80 - 4d + 3d = 8.60
\]
\[
9.80 - d = 8.60
\]

### Step 4: Solve for $d$
Now solve for $d$:

\[
9.80 - 8.60 = d
\]
\[
d = 1.20
\]

### Step 5: Find $c$
Now that we know $d = 1.20$, substitute this into $c = 4.90 - 2d$:

\[
c = 4.90 - 2(1.20)
\]
\[
c = 4.90 - 2.40
\]
\[
c = 2.50
\]

### Final Answer:
The cost of one cup of coffee is **$2.50** (option A).

---

Do you need any further clarification or a detailed breakdown? 

Here are 5 related questions:
1. How can you verify the solution by substituting back into both equations?
2. What is the cost of one doughnut based on this solution?
3. How would the solution change if the second equation were different?
4. What are some other methods to solve systems of linear equations?
5. How can you solve a system of equations graphically?

**Tip:** When solving systems of equations, always check your final answer by substituting it back into the original equations!

Two customers purchased coffee and doughnuts at a coffee shop. The system of equations below can be used to find the cost of a cup of coffee. c + 2d = 4.90, 2c + 3d = 8.60. What is the cost of 1 cup of coffee?

Learn how to solve a system of equations to find the cost of a cup of coffee and a doughnut. This problem involves two linear equations and uses the substitution method. Ideal for students in Grades 7-10.

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