Answer:
Cup of coffee: 0.50$
Piece of cake: 0.45$
Step-by-step explanation:
To solve this problem, we call:
c = the cost of 1 cup of coffee
p = the cost of 1 piece of cake
Here we know that:
7 cups of coffee and 4 pieces of cake cost $5.3, so we can write
(1)
5 cups of coffee and 2 pieces of cake cost $3.4, so we can write
(2)
So we have a system of 2 equations in 2 unknown variables to solve.
We start by multiplying eq(2) by 2, so we get:
(3)
Now we subtract eq(1) from eq(3), and we get:

So the cost of 1 cup of coffee is 0.5$.
Now we can substitute the value of c in eq(2) to find the value of p:

So, the price of 1 piece of cake is 0.45$.