Kilometers of the journey

A cyclist travelled 199 km over three days. On the first day, he travelled four times as far as on the second day, and on the second day, he travelled 7 km less than on the third day. How many kilometres did he travel each day?

Final Answer:

a =  128 km
b =  32 km
c =  39 km

Step-by-step explanation:

$$\begin{gathered} a+b+c=199 \\ a=4b \\ b=c-7 \\ 4b+b+(b+7)=199 \\ 4\cdot b+b+(b+7)=199 \\ 6b=192 \\ b=\frac{192}{6}=32 \\ b=32 \\ a=4\cdot b=4\cdot 32=128\text{km} \end{gathered}$$

$$\begin{gathered} c=b+7=32+7=39=39\text{km} \\ \text{ Verifying Solution: } \\ s=a+b+c=128+32+39=199\text{km} \end{gathered}$$

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