Paper 2 - Calculators are allowed. 1. Mdm Farah baked an equal number of cupcakes and cookies. After she sold 32 cupcakes and 20 cookies, the number of cupcakes left was \( \frac{4}{7} \) of the number of cookies left. How many cookies did she bake at first?

Let's assume Mdm Farah baked \( x \) cupcakes and \( x \) cookies. After selling 32 cupcakes and 20 cookies, she has \( x - 32 \) cupcakes and \( x - 20 \) cookies left. According to the problem, the number of cupcakes left is \( \frac{4}{7} \) of the number of cookies left, which gives us the equation: \[ x - 32 = \frac{4}{7}(x - 20) \] To eliminate the fraction, multiply both sides by 7: \[ 7(x - 32) = 4(x - 20) \] This simplifies to: \[ 7x - 224 = 4x - 80 \] Rearranging gives us: \[ 7x - 4x = 224 - 80 \\ 3x = 144 \\ x = 48 \] Thus, Mdm Farah initially baked 48 cookies.