Three-day trip

On a three-day trip, cyclists traveled 30% of the total route on the first day, 3/5 of the rest on the second day, and 35 km on the third day. Thus, cyclists traveled 30% of the total route on the first day, 3/5 of the rest on the second day, and 35 km on the third day. Thus, cyclists traveled 30% of the total route on the first day, 3/5 of the rest on the second day, and 35 km on the third day. How many kilometers did cyclists travel each day, and how many?

Correct answer:

a =  37.5 km
b =  52.5 km
c =  35 km
s =  125 km

Step-by-step explanation:

$$\begin{gathered} c=35\text{km} \\ q=30\%=\frac{30}{100}=\frac{3}{10}=0.3 \\ a+b+c=s \\ a=q\cdot s \\ b=\frac{3}{5}\cdot (s-a) \\ q\cdot s+\frac{3}{5}\cdot (s-q\cdot s)+c=s \\ 0.3\cdot s+\frac{3}{5}\cdot (s-0.3\cdot s)+35=s \\ 0.3\cdot s+3/5\cdot (s-0.3\cdot s)+35=s \\ 1.4s=175 \\ s=\frac{175}{1.4}=125 \\ s=125 \\ a=q\cdot s=0.3\cdot 125=\frac{75}{2}\text{km}=37.5\text{km} \end{gathered}$$

$b=\frac{3}{5}\cdot (s-a)=\frac{3}{5}\cdot (125-37.5)=\frac{105}{2}\text{km}=52.5\text{km}$

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