Collected 7298

Ema collected 770 kg of waste paper during the school year, while her friend Patrik collected 15% less. During the following school year, Ema collected exactly as much as Patrik did last year, but Patrik managed to collect 15% more than Eme. Which one collected more during both school years?

Correct answer:

x = ema

Step-by-step explanation:

$$\begin{gathered} m_1=770\text{kg} \\ {p}_1=(1-\frac{15}{100})\cdot m_1=(1-\frac{15}{100})\cdot 770=\frac{1309}{2}=654\frac{1}{2}=654.5\text{kg} \\ {m}_2=p_1=\frac{1309}{2}=654\frac{1}{2}=654.5\text{kg} \\ {p}_2=(1+\frac{15}{100})\cdot m_2=(1+\frac{15}{100})\cdot 654.5=\frac{30107}{40}=752\frac{27}{40}=752.675\text{kg} \\ m=m_1+m_2=770+654.5=\frac{2849}{2}=1424\frac{1}{2}=1424.5\text{kg} \\ p=p_1+p_2=\frac{1309}{2}+\frac{30107}{40}=\frac{26180}{40}+\frac{30107}{40}=\frac{26180+30107}{40}=\frac{56287}{40}=1407\frac{7}{40}=1407.175\text{kg} \\ p<m \\ x=ema \end{gathered}$$

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