Children's 61804

Three children's scooters cost a total of 179 euros. The first was 18% more expensive than the second. The third was 20 euros more expensive than the second. Determine the price of the first scooter.

Correct answer:

a =  59 Eur

Step-by-step explanation:

$$\begin{gathered} p=18\%=\frac{18}{100}=\frac{9}{50}=0.18 \\ a+b+c=179 \\ a=b+p\cdot b \\ c=20+b \\ a+b+c=179 \\ a=b+0.18\cdot b \\ c=20+b \\ a+b+c=179 \\ a-1.18b=0 \\ b-c=-20 \\ Row2-Row1\to Row2 \\ a+b+c=179 \\ -2.18b-c=-179 \\ b-c=-20 \\ Row3-\frac{1}{-2.18}\cdot Row2\to Row3 \\ a+b+c=179 \\ -2.18b-c=-179 \\ -1.459c=-102.11 \\ c=\frac{-102.11009174}{-1.4587156}=70 \\ b=\frac{-179+c}{-2.18}=\frac{-179+70}{-2.18}=50 \\ a=179-b-c=179-50-70=59 \\ a=59 \\ b=50 \\ c=70 \end{gathered}$$

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