Respuesta :
Answer: 30% of the cakes were sponge cakes.
Step-by-step explanation: We are given that 50% of the cakes Jenny baked that week were party cakes, one-fifth were fruit cakes and the remainder were sponge cakes.
We are to find the percentage of cakes that were sponge cakes.
Let n represents the number of cakes that Jenny baked.
According to the given information, we have
[tex]C_p=50\%\times n=\dfrac{50}{100}\times n=\dfrac{n}{2},\\\\\\C_f=\dfrac{1}{5}\times n=\dfrac{n}{5}.[/tex]
Therefore, the number of sponge cakes is given by
[tex]C_s=n-C_p-C_f=n-\dfrac{n}{2}-\dfrac{n}{5}=\dfrac{10-5n-2n}{10}=\dfrac{3n}{10}.[/tex]
Therefore, the percentage of cakes that were sponge cakes is given by
[tex]C_s\%=\dfrac{\frac{3n}{10}}{n}\times100\%=30\%.[/tex]
Thus, 30% of the cakes were sponge cakes.
