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. About the author Charlotte

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 Reply

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 Reply

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:## 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