Question

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 1

150 one point throws, 165 two points throws and 110 three points throws

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

`x=y-15`

so the number of two points throws
`=x+15`

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

`y=2z-55\\ \\2z=y+55\\ \\2z=x+15+55\\ \\2z=x+70\\ \\z=(1)/(2)x+35`

so the number of three points throws
`=(1)/(2)x+35`

The total score is 810 points, so

`x\cdot 1+(x+15)\cdot 2+\left((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\\ \\(1)/(2)x+35=(1)/(2)\cdot 150+35=75+35=110`