Daniel bakes 420 cakes - Edexcel - GCSE Maths - Question 4 - 2017 - Paper 3

To find the number of banana cakes, we calculate:

[ \text{Number of Banana Cakes} = 0.35 \times 420 = 147 ]

Thus, Daniel bakes 147 banana cakes.

Let the number of chocolate cakes be represented as ( c ).

The total number of cakes is composed of vanilla, banana, lemon, and chocolate cakes:

[ 120 + 147 + \text{Lemon Cakes} + c = 420 ]

We also know the ratio of lemon cakes to chocolate cakes is 4:5, hence we can express:

[ \text{Lemon Cakes} = \frac{4}{5}c ]

Substituting in, we have:

[ 120 + 147 + \frac{4}{5}c + c = 420 ]

Combining like terms:

[ 267 + \frac{9}{5}c = 420 ]

Thus,

[ \frac{9}{5}c = 420 - 267 ]
[ \frac{9}{5}c = 153 ]

Solving for ( c ) gives:

[ c = 153 \times \frac{5}{9} \approx 85 ]

Therefore, Daniel bakes approximately 85 chocolate cakes.

We can now find the number of lemon cakes using the ratio established earlier. Since ( c = 85 ), we find:

[ \text{Lemon Cakes} = \frac{4}{5} \times 85 = 68 ]

Thus, the total number of lemon cakes Daniel bakes is 68.