at joes cafe, one cup of coffee and three doughnuts cost $3.50, and two cups of coffee and two doughnuts cost $3.80. what is the cost of one doughnut
Let the cost of one cup of coffee be C and the cost of one doughnut be D.
From the information given, we can set up a system of equations:
C + 3D = 3.50 (equation 1)
2C + 2D = 3.80 (equation 2)
To simplify equation 2, we can divide it by 2:
C + D = 1.90 (equation 3)
Now we have a system of equations with 2 variables.
We can solve equation 3 for C:
C = 1.90 - D
Substituting this into equation 1, we get:
(1.90 - D) + 3D = 3.50
1.90 + 2D = 3.50
2D = 3.50 - 1.90
2D = 1.60
D = 1.60/2
D = 0.80
Therefore, the cost of one doughnut is $0.80.
Let's assume that the cost of one cup of coffee is C and the cost of one doughnut is D.
From the problem, we have the following information:
1C + 3D = $3.50 (equation 1)
2C + 2D = $3.80 (equation 2)
To solve for the cost of one doughnut (D), we need to eliminate the variable C. We can achieve this by multiplying equation 2 by 2 and equation 1 by -3, then adding the resulting equations together.
Multiply equation 2 by 2:
2 * (2C + 2D) = 2 * $3.80
4C + 4D = $7.60 (equation 3)
Multiply equation 1 by -3:
-3 * (1C + 3D) = -3 * $3.50
-3C - 9D = -$10.50 (equation 4)
Now, add equations 3 and 4:
(4C + 4D) + (-3C - 9D) = $7.60 + (-$10.50)
C - 5D = -$2.90
Now, let's solve for C in terms of D:
C = -$2.90 + 5D
We still need more information to determine the specific value for D.