At a business meeting at panera bread company the bill for two cappuccinos and there house lattes was $14.55. At another table the bill for one cappuccino and two house lattes was $8.77. How much did each type of beverage cost? I'm not sure how this would be worked out. Can you please show me the steps of what and how I should do this?
2 c + 3 L = 14.55
1 c + 2 L = 8.77 multiply second one by 2
2 c + 3 L = 14.55
2 c + 4 L = 17.54
-------------------- subtract
-1 L = - 2.99
L = 2.99
then c = 8.77-2L = 2.79
Sure, let's try to figure out the cost of each type of beverage. Let's represent the cost of a cappuccino as "C" and the cost of a house latte as "H".
According to the given information, we have two equations:
Equation 1: 2C + H = 14.55
Equation 2: C + 2H = 8.77
To solve this system of equations, we can use either substitution or elimination method. Let's use the elimination method in this case.
Multiply Equation 1 by 2:
4C + 2H = 29.10
Now, subtract Equation 2 from the new equation:
4C + 2H - (C + 2H) = 29.10 - 8.77
3C = 20.33
Divide both sides by 3 to isolate C:
C = 20.33 / 3
C ≈ 6.78
Now, substitute the value of C into either Equation 1 or Equation 2 to solve for H. Let's use Equation 1:
2(6.78) + H = 14.55
13.56 + H = 14.55
H = 14.55 - 13.56
H ≈ 0.99
So, each cappuccino costs approximately $6.78 and each house latte costs approximately $0.99.
To solve this problem, we can use a system of equations. Let's represent the cost of a cappuccino as "C" and the cost of a house latte as "H".
Step 1: Write the equations based on the given information:
Equation 1: 2C + 2H = 14.55 (bill for two cappuccinos and two house lattes)
Equation 2: 1C + 2H = 8.77 (bill for one cappuccino and two house lattes)
Step 2: Solve the system of equations by either substitution or elimination method. Let's use the elimination method to solve this system:
Multiply Equation 2 by 2 to eliminate the "C" term:
2C + 4H = 17.54
Step 3: Subtract Equation 1 from Equation 2 to eliminate the "C" term:
(2C + 4H) - (2C + 2H) = 17.54 - 14.55
2H = 2.99
Step 4: Solve for "H" by dividing both sides of the equation by 2:
H = 2.99 / 2
H = 1.495
Step 5: Substitute the value of "H" into either Equation 1 or Equation 2 to find the value of "C". Let's use Equation 1:
2C + 2(1.495) = 14.55
2C + 2.99 = 14.55
2C = 14.55 - 2.99
2C = 11.56
C = 11.56 / 2
C = 5.78
Step 6: Solve for both beverage costs. The cost of a cappuccino (C) is $5.78, and the cost of a house latte (H) is $1.495.
To find the cost of each type of beverage, we can set up a system of equations based on the given information. Let's assume the cost of a cappuccino is represented by "C" and the cost of a house latte is represented by "H."
Equation 1:
2C + 3H = 14.55
Equation 2:
C + 2H = 8.77
We have two equations and two variables (C and H). Now, we can use a method called substitution or elimination to solve the system of equations. Let's use the substitution method.
1. Solve Equation 2 for C:
C = 8.77 - 2H
2. Substitute the value of C from Equation 2 into Equation 1:
2(8.77 - 2H) + 3H = 14.55
3. Simplify and solve for H:
17.54 - 4H + 3H = 14.55
17.54 - H = 14.55
-H = 14.55 - 17.54
-H = -2.99
4. Multiply both sides of the equation by -1 to isolate H:
H = 2.99
Now that we have the value of H, we can substitute it back into Equation 2 to find the value of C:
C + 2(2.99) = 8.77
C + 5.98 = 8.77
C = 8.77 - 5.98
C = 2.79
So, the cost of a cappuccino is $2.79, and the cost of a house latte is $2.99.