Question

The cost of a cake is twice that of a cup of tea.

1 cake and 5 cups of tea cost £21.
How much does a cake cost?

Answer 1

Cake: £6

Explanation:

1c = 2t Eq. 1

1c + 5t = 21 Eq. 2

c = cost of a cake

t = cost of a cup of tea

Replacing Eq. 1 in Eq 2:

2t + 5t = 21

7t = 21

t = 21/7

t = 3

From Eq. 1:

c = 2t

c = 2*3

c = 6

Check:

From Eq. 2:

c + 5t = 21

6 + 5*3 = 21

6 + 15 = 21

Answer 2

The cake cost $6.00

Explanation:

Let c = the cost of the cake

Let t = the cost of the tea

c = 2t

c + 5t = 21 Substitute 2t for c

2t + 5t = 21 Combine like terms

7t = 21 Divide both sides by 7

`(7t)/(7)` =
`(21)/(7)`

t = 3

A cup of tea costs $3.00

c = 2t Substitute 3 for t

c = 2(3)

c = 6

A cake costs $6.00