7 cups of coffee and 4 pieces of cake cost $5.3 while 5 cups of coffee and 2 pieces of cake cost $3.4. Find the cost of one cup of coffee and one piece of cake.

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$.