Three-quarters 25931

Jarek went strawberry picking for a day. In the morning, he collected two-fifths of the required amount; in the afternoon, he collected 5 kg less than in the morning. In total, he collected three-quarters of the required amount. How many kilograms of strawberries does he have to collect before the end of the brigade?

Correct answer:

x =  25 kg

Step-by-step explanation:

$$\begin{gathered} a=2/5\cdot m \\ b=a-5 \\ a+b=3/4\cdot m \\ 5a-2m=0 \\ a-b=5 \\ 4a+4b-3m=0 \\ Row2-\frac{1}{5}\cdot Row1\to Row2 \\ 5a-2m=0 \\ -b+0.4m=5 \\ 4a+4b-3m=0 \\ Row3-\frac{4}{5}\cdot Row1\to Row3 \\ 5a-2m=0 \\ -b+0.4m=5 \\ 4b-1.4m=0 \\ Pivot:Row2\leftrightarrow Row3 \\ 5a-2m=0 \\ 4b-1.4m=0 \\ -b+0.4m=5 \\ Row3-\frac{-1}{4}\cdot Row2\to Row3 \\ 5a-2m=0 \\ 4b-1.4m=0 \\ 0.05m=5 \\ m=\frac{5}{0.05}=100 \\ b=\frac{0+1.4m}{4}=\frac{0+1.4\cdot 100}{4}=35 \\ a=\frac{0+2m}{5}=\frac{0+2\cdot 100}{5}=40 \\ a=40 \\ b=35 \\ m=100 \\ x=m-a-b=100-40-35=25\text{kg} \end{gathered}$$

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