Water in vegetables

Tomatoes in the store contain 99% water. After being transported to the shop, they were slightly dried and contained only 98% of water. How many kgs of tomatoes are in the store if there were 300 kg in stock?`

Correct answer:

x =  150 kg

Step-by-step explanation:

$$\begin{gathered} r_1=99\%=\frac{99}{100}=0.99 \\ {r}_2=98\%=\frac{98}{100}=\frac{49}{50}=0.98 \\ m=300\text{kg} \\ S=(1-r_1)\cdot m=(1-0.99)\cdot 300=3\text{kg} \\ S=(1-r_2)\cdot x \\ x=S/(1-r_2)=3/(1-0.98)=150=150\text{kg} \\ \text{ Verifying Solution: } \\ {w}_1=m-S=300-3=297\text{kg} \\ {w}_2=x-S=150-3=147\text{kg} \\ {p}_2=100\cdot \frac{w_2}{x}=100\cdot \frac{147}{150}=\frac{100\cdot 147}{150}=\frac{14700}{150}=98\% \end{gathered}$$

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