solve the equation of 5c+9s+7k=40.84

Question

solve the following:

week 1 : 5 coffees, 9 sandwiches and 7 cakes cost £20.62

week 2: 3 coffees, 5 sandwiches and 4 cakes cost £11.66

week 3: 4 coffees, 2 sandwiches and 5 cakes cost £8.56

How much is each item?

Answer 1

c=cost of coffee, s=cost of sandwich, k=cost of cake.

(1) 5c+9s+7k=20.62

(2) 3c+5s+4k=11.66

(3) 4c+2s+5k=8.56

4(1)=20c+36s+28k=82.48; 7(2)=21c+35ss+28k=81.62;

(4) 4(1)-7(2)=-c+s=0.86.

5(2)=15c+25s+20k=58.30; 4(3)=16c+8s+20k=34.24;

(5) 5(2)-4(3)=-c+17s=24.06.

From (4), -c=0.86-s, so (5) becomes 0.86-s+17s=24.06, 16s=23.20, s=£1.45.

c=s-0.86=1.45-0.86=£0.59.

From (3), 4c+2s+5k=2.36+2.90+5k=8.56, 5k=3.30, k=£0.66.

Coffee costs £0.59, sandwich costs £1.45, cake costs £0.66.