The basketball team scored a total of $86$ points. Josiah scored one-half the points of Jared. $\newline$ Maricella scored two less than Jared. Jared and Connie both scored the same number of points and Bryan scored twice as many as Connie. How many points did each player score?

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Q. The basketball team scored a total of

86

points. Josiah scored one-half the points of Jared.

\newline

Maricella scored two less than Jared. Jared and Connie both scored the same number of points and Bryan scored twice as many as Connie. How many points did each player score?

Denote Scores: Let's denote the number of points Jared scored as $J$ . According to the problem, Josiah scored one-half the points of Jared, so Josiah's score is $\frac{J}{2}$ . Maricella scored two less than Jared, so her score is $J - 2$ . Jared and Connie scored the same number of points, so Connie's score is also $J$ . Bryan scored twice as many as Connie, so Bryan's score is $2J$ . The total points scored by the team is $86$ . We can set up an equation to represent this information: $\newline$ $\frac{J}{2}$ (Josiah) + $J$ (Jared) + $(J - 2)$ (Maricella) + $J$ (Connie) + $2J$ (Bryan) = $86$
Simplify Equation: Combine like terms to simplify the equation: $\newline$ $\frac{J}{2} + J + J - 2 + J + 2J = 86$ $\newline$ This simplifies to: $\newline$ $5.5J - 2 = 86$
Isolate Terms with J: Add $2$ to both sides of the equation to isolate the terms with J: $\newline$ $5.5J - 2 + 2 = 86 + 2$ $\newline$ $5.5J = 88$
Solve for J: Divide both sides by $5.5$ to solve for $J$ : $\newline$ $\frac{5.5J}{5.5} = \frac{88}{5.5}$ $\newline$ $J = 16$
Find Player Scores: Now that we have the value for $J$ , we can find the scores for each player: $\newline$ Josiah's score is $\frac{J}{2} = \frac{16}{2} = 8$ $\newline$ Maricella's score is $J - 2 = 16 - 2 = 14$ $\newline$ Connie's score is $J = 16$ $\newline$ Bryan's score is $2J = 2 \times 16 = 32$