Matej 2

Matej, Marko, Milan, and Matúš had a total of 205 football player cards with signatures. Marko has four times more than Matej. Matúš had two times less than Marko. Milan had 20 cards less than Matúš. How many cards did each have?

Correct answer:

a =  25
b =  100
c =  30
d =  50

Step-by-step explanation:

$$\begin{gathered} a+b+c+d=205 \\ b=4a \\ d=b/2 \\ c=d-20 \\ a+b+c+d=205 \\ a+4a+(d-20)+b/2=205 \\ a+4a+(b/2-20)+b/2=205 \\ a+4a+(4a/2-20)+4a/2=205 \\ a+4\cdot a+(4\cdot a/2-20)+4\cdot a/2=205 \\ 18a=450 \\ a=\frac{450}{18}=25 \\ a=25 \end{gathered}$$

$b=4\cdot a=4\cdot 25=100$

$$\begin{gathered} d=b/2=100/2=50 \\ c=d-20=50-20=30 \end{gathered}$$

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