Sarah Liskow was the top scorer in a​ women's professional basketball league for the 2006 regular​ season, with a total of 810 points. The number of​ two-point field goals that Sarah made was 55 less than double the number of​ three-point field goals she made. The number of free throws​ (each worth one​ point) she made was 15 less than the number of​ two-point field goals she made. Find how many free​ throws, two-point field​ goals, and​ three-point field goals Sarah Liskow made during the 2006 regular season

Answer:150 one point throws, 165 two points throws and 110 three points throwsStep-by-step explanation:Let x be the number of free (one point) throws.The number of free throws​ Sarah made was 15 less than the number of​ two-point field goals she made. If y is the number of two points throws, then[tex]x=y-15[/tex]so the number of two points throws [tex]=x+15[/tex]The number of​ two-point field goals that Sarah made was 55 less than double the number of​ three-point field goals she made. If z is the number of three points throws, then[tex]y=2z-55\\ \\2z=y+55\\ \\2z=x+15+55\\ \\2z=x+70\\ \\z=\dfrac{1}{2}x+35[/tex]so the number of three points throws [tex]=\dfrac{1}{2}x+35[/tex]The total score is 810 points, so[tex]x\cdot 1+(x+15)\cdot 2+\left(\dfrac{1}{2}x+35\right)\cdot 3=810\\ \\x+2x+30+1.5x+105=810\\ \\4.5x=810-30-105\\ \\4.5x=675\\ \\x=150\\ \\x+15=150+15=165\\ \\\dfrac{1}{2}x+35=\dfrac{1}{2}\cdot 150+35=75+35=110[/tex]