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 cup of coffee

Answer 1

Let's assume the cost of one cup of coffee is 'x' dollars and the cost of one doughnut is 'y' dollars.

According to the given information:
1x + 3y = 3.50 ...(Equation 1)
2x + 2y = 3.80 ...(Equation 2)

To solve this system of equations, let's multiply Equation 1 by 2 and Equation 2 by -1:
2(1x + 3y) = 2(3.50)
-1(2x + 2y) = -1(3.80)

2x + 6y = 7.00 ...(Equation 3)
-2x - 2y = -3.80 ...(Equation 4)

Now, let's add Equation 3 and Equation 4 together:
(2x + 6y) + (-2x - 2y) = 7.00 + (-3.80)
4y = 3.20

Now, solving for 'y':
y = 3.20/4
y = 0.80

Now, substitute the value of 'y' in Equation 1:
1x + 3(0.80) = 3.50
1x + 2.40 = 3.50
1x = 3.50 - 2.40
1x = 1.10

Therefore, the cost of one cup of coffee is $1.10.