Question

Q#5(a) Seven cups of coffee and 4 pieces of toast cost $10.6. 5 cups of coffee and 4 pieces of toast cost
$8.60. Find the cost of each item.​

Answer 1

Answer:

We can set up a system of equations to solve this. Calling the price of a cup of coffee C, and the price of a cup of tea T, we get

(1) 4C+4T=12

(2) 3C=2T

If we divide both sides of (1) by 4 we get

(3) C+T=3

We want to find 5C+5T, so to do that we can multiply both sides of (3) by 5 to get

(4) 5C+5T=15

Therefore the answer is $15

We can check this by working out the individual prices of a cup of tea or coffee and substituting them back into (4):

We can substitute 2 x (2) into (1) to get

(5) 4C+6C=12

ie 10C=12, so C = $1.20

Then from 2, 3 x 1.20=2T, so T=$1.80

Substituting into (4), we find that 5 x 1.20 + 5 x 1.80= 6 + 9 = $15

Answer 2

Answer:

4c+4t=12

3c=2t

c=2/3t

Sub this into orginal equation

4(2/3t)+4t4t=12

8/3t+4t=12

20/3t=12

t=36/20

Therefore t=1.8

Sub this into 3c=3.6

Therefore c=1.2

So a cup of coffee is $1.20 and a cup of tea is$1.80