Question

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.

Answer 1

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

$7c+4p=5.3$ (1)

5 cups of coffee and 2 pieces of cake cost $3.4, so we can write

$5c+2p=3.4$ (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:

$10c+4p=6.8$ (3)

Now we subtract eq(1) from eq(3), and we get:

$(10c-7c)+(4p-4p)=6.8-5.3\\3c=1.5\\c=\frac{1.5}{3}=0.5$

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:

$5(0.5)+2p = 3.4\\2.5 +2p = 3.4\\2p=3.4-2.5=0.9\\p=\frac{0.9}{2}=0.45$

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