The system of equations appears to be missing some equality signs and is somewhat unclear. Based on what I interpret from your message, it seems there are two customers who made two transactions that we can represent as follows:
-
The first customer's total cost is for \( x \) cups of coffee and \( 2 \) doughnuts: \[ x + 2d = 4.90 \]
-
The second customer's total cost is for \( 2x \) cups of coffee and \( 3 \) doughnuts: \[ 2x + 3d = 8.60 \]
Now we can solve this system of equations for \( c \) (the cost of one cup of coffee) and \( d \) (the cost of one doughnut).
Step 1: Rearranging the equations
-
From the first equation, we have: \[ x + 2d = 4.90 \quad \text{(1)} \]
-
From the second equation, we have: \[ 2x + 3d = 8.60 \quad \text{(2)} \]
Step 2: Solve for \( x \) in terms of \( d \) using equation (1) \[ x = 4.90 - 2d \quad \text{(3)} \]
Step 3: Substitute equation (3) into equation (2) Now substitute \( x \) from equation (3) into equation (2): \[ 2(4.90 - 2d) + 3d = 8.60 \] Expanding this, \[ 9.80 - 4d + 3d = 8.60 \] Combine like terms: \[ 9.80 - d = 8.60 \] Now isolate \( d \): \[ -d = 8.60 - 9.80 \] \[ -d = -1.20 \] \[ d = 1.20 \]
Step 4: Substitute \( d \) back into equation (3) to find \( x \) Now use \( d = 1.20 \) in equation (3): \[ x = 4.90 - 2(1.20) \] Calculate \( x \): \[ x = 4.90 - 2.40 = 2.50 \]
Now we have the quantities:
- \( x = 2.50 \) (the cost of one cup of coffee)
Answer: The cost of 1 cup of coffee is $2.50.
1 answer