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$.

aloha~! my name is zalgo and i am here to you out on this amazing day. to answer your question, yes, nonzero numbers can have a greatest common factor and that would be 1. still don't get it? let me considering every number is divisible by 1 and hence every number has 1 as a factor of theirs. so, if 2 nonzero numbers didn't share any gcf (greatest common factor), they would still have a factor in common and that would be 1.

i hope that this ! : p

"stay and stay proud! " - zalgo

(by the way, do you mind marking me as brainliest? i'd greatly appreciate it! mahalo! x3)