At the coffee shop, two coffees and one latte cost $10.50. Three coffees and two lattes cost $17.00. What is the cost of one coffee?

Let the price of coffee be x and the price of latte be y.

Thus forming the equations given the information we shall have:

2x+y=10.50

y=10.50-2x ... i

3x+2y=17 ... ii

plugging i in ii we get:

3x+2 (10.50-2x) = 17

3x+21-4x=17

3x-4x=17-21

-x=-4

thus

x=4

Thus the cost of coffee is $4

thus the cost of latte will be:

y=10.50-2 (4)

y=10.50-8

y=2.5

Price of latte is $2.5