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During game 3 of the basketball championships, San Antonio scored 97 points consisting of 2-point and 3-point baskets. If San Antonio made a total of 45 baskets, how many of each type did they made? A 2-point baskets: 7 3-point baskets: 38 B 2-point baskets: 38 3-point baskets: 7 с 2-point baskets: 42 3-point baskets: 3 D 2-point baskets: 3 3-point baskets: 42 A. A В. B с. С D D

Respuesta :

We have the following:

To solve the problem we must plan a system of equations of two equations with two unknowns

let x numbers of 2-point baskets

let y numbers of 3-point backets

[tex]\begin{gathered} x+y=45 \\ 2x+3y=97 \end{gathered}[/tex]

solving the system:

[tex]\begin{gathered} y=45-x \\ 2x+3\cdot(45-x)=97 \\ 2x+135-3x=97 \\ -x=97-135 \\ x=38 \end{gathered}[/tex]

for y:

[tex]\begin{gathered} y=45-38 \\ y=7 \end{gathered}[/tex]

The answer is 38 2-point baskets and 7 3-point baskets, the option B

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