Matej 2

Matthew, Mark, Miles, and Matt had a total of 205 football player cards with signatures. Mark has four times more than Matthew. Matt had twice less than Mark. Miles had 20 fewer cards than Matthew. How many cards did each of them 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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