Matej 2

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

Final 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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