3 doughnuts and 2 cakes cost £7. 5 doughnuts and 4 cakes cost £13. what’s the cost of a doughnut? what’s the cost of a cake?

Answer 1

d=doughnuts

c=cakes

3d+2c=7 <----Eq(1)

5d+4c=13 <----Eq(2)

So, take Eq(1) and solve for either d or c:

3d+2c=7

3d=7-2c

d=(7-2c)/3

Now we plug it into Eq(2) and solve for c:

5((7-2c)/3)+4c=13

(35-10c)/3+4c=13

(35/3)-(10c/3)+4c=13

-(10c/3)+4c=13-(35/3) <---- we combine like terms and get combine denominators

-(10c/3)+(12c/3)=(39/3)-(35/3)

2c/3=4/3

2c=4

c=2

Cakes cost £2.

Now plug in c into either Eq(1) or Eq(2):

3d+2c=7

3d+2(2)=7

3d=7-4

3d=3

d=1

Doughnuts cost £1.

You can check to see if both equations work and they do!