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A basketball player hit the basket eighteentimes during the game. He scored a totalof 30 points, two points for each field goaland one point for each free throw. If hethrew 6 more field goals than free throws,how many field goals did he make? Howmany free throws did he make?

Sagot :

[tex]\begin{gathered} x=field\text{ g}oal \\ y=free\text{ throw} \\ 2x+y=30 \\ \text{also} \\ x=y+6 \\ \text{Then the system is} \\ 2x+y=30\text{ (1)} \\ x=y+6\text{ (2)} \\ U\sin g\text{ (2) in (1)} \\ 2(y+6)+y=30 \\ 2y+12+y=30 \\ 2y+y=30-12 \\ 3y=18 \\ y=\frac{18}{3} \\ y=6 \\ \text{hence} \\ x=6+6 \\ x=12 \\ \text{therefore} \\ He\text{ }make\text{ 6 fre}e\text{ throw}s \end{gathered}[/tex]

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