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
[tex]7c+4p=5.3[/tex] (1)
5 cups of coffee and 2 pieces of cake cost $3.4, so we can write
[tex]5c+2p=3.4[/tex] (2)
So we have a system of 2 equations in 2 unknown variables to solve.
We start by multiplying eq(2) by 2, so we get:
[tex]10c+4p=6.8[/tex] (3)
Now we subtract eq(1) from eq(3), and we get:
[tex](10c-7c)+(4p-4p)=6.8-5.3\\3c=1.5\\c=\frac{1.5}{3}=0.5[/tex]
So the cost of 1 cup of coffee is 0.5$.
Now we can substitute the value of c in eq(2) to find the value of p:
[tex]5(0.5)+2p = 3.4\\2.5 +2p = 3.4\\2p=3.4-2.5=0.9\\p=\frac{0.9}{2}=0.45[/tex]
So, the price of 1 piece of cake is 0.45$.
