Cocoa bundt cake

Grandma was baking a cocoa bundt cake. According to the recipe, she was to mix flour, sugar, cocoa, and butter in the ratio 6:5:2:3.
Calculate how much sugar grandma had to use if she put 70 grams of cocoa into the dough.
Her granddaughter decided to also bake a bundt cake according to grandma's recipe. How many grams of flour did the granddaughter put into the dough if the total weight of all the above-mentioned ingredients was 720 grams?

Final Answer:

b =  175 g
a₂ =  270 g

Step-by-step explanation:

$$\begin{gathered} a:b:c:d=6:5:2:3 \\ c=70\text{g} \\ b:c=5:2 \\ b=c\cdot \frac{5}{2}=70\cdot \frac{5}{2}=\frac{70\cdot 5}{2}=\frac{350}{2}=175\text{g} \end{gathered}$$

$$\begin{gathered} m_2=720\text{g} \\ {m}_2=a_2+b_2+c_2+d_2 \\ {m}_2=(6+5+2+3)x \\ x=m_2/(6+5+2+3)=720/(6+5+2+3)=45\text{g} \\ {a}_2=6\cdot x=6\cdot 45=270\text{g} \end{gathered}$$

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