Two customers purchased coffee and doughnuts at a coffee shop. Each cup of coffee costs the same amount, and each doughnut costs the same amount. The system of equations below can be used to find c
, the cost of a cup of coffee, and d
, the cost of a doughnut.
 
c+2d=4.90
2c+3d=8.60

What is the cost of 1
 cup of coffee?
A.$2.50

B.$1.20

C.$4.90

D.$3.70


To find the cost of one cup of coffee, we can solve the system of equations using substitution or elimination.

The system is:
1. $ c + 2d = 4.90 $  (Equation 1)
2. $ 2c + 3d = 8.60 $  (Equation 2)

### Step 1: Solve Equation 1 for $ c $
From Equation 1:
\[
c = 4.90 - 2d
\]

### Step 2: Substitute into Equation 2
Now, substitute $ c = 4.90 - 2d $ into Equation 2:
\[
2(4.90 - 2d) + 3d = 8.60
\]

### Step 3: Simplify the equation
Distribute the $ 2 $:
\[
9.80 - 4d + 3d = 8.60
\]
Simplify further:
\[
9.80 - d = 8.60
\]

### Step 4: Solve for $ d $
Subtract 9.80 from both sides:
\[
-d = 8.60 - 9.80
\]
\[
-d = -1.20
\]
\[
d = 1.20
\]
So, the cost of a doughnut is $ d = 1.20 $.

### Step 5: Solve for $ c $
Substitute $ d = 1.20 $ back into the expression for $ c $ from Step 1:
\[
c = 4.90 - 2(1.20)
\]
\[
c = 4.90 - 2.40
\]
\[
c = 2.50
\]

Thus, the cost of one cup of coffee is **$2.50**, which corresponds to **Option A**.

Would you like any additional details or clarifications?

---

Here are five related questions:
1. How would you solve the system using the elimination method?
2. What if the cost of a cup of coffee increased by 10%—what would be the new cost?
3. How can you check if the values of $ c $ and $ d $ are correct?
4. What would be the cost of 3 cups of coffee and 5 doughnuts?
5. Can you write a similar problem with different prices for coffee and doughnuts?

**Tip:** When solving systems of equations, substitution is often easier when one variable is already isolated or can be easily solved for.

Two customers purchased coffee and doughnuts at a coffee shop. Each cup of coffee costs the same amount, and each doughnut costs the same amount. The system of equations below can be used to find c, the cost of a cup of coffee, and d, the cost of a doughnut.

c + 2d = 4.90
2c + 3d = 8.60

What is the cost of 1 cup of coffee?
A. $2.50
B. $1.20
C. $4.90
D. $3.70

Solve the system of equations to find the cost of one cup of coffee and one doughnut. Using algebraic techniques such as substitution, learn how to work through real-world examples involving prices of goods. Suitable for students in Grades 8-10.

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