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The basketball team scored a total of 86 points. Josiah scored one-half the points of Jared. 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?

The basketball team scored a total of 8686 points. Josiah scored one-half the points of Jared.\newlineMaricella 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 8686 points. Josiah scored one-half the points of Jared.\newlineMaricella 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?
  1. Denote Scores: Let's denote the number of points Jared scored as JJ. According to the problem, Josiah scored one-half the points of Jared, so Josiah's score is J2\frac{J}{2}. Maricella scored two less than Jared, so her score is J−2J - 2. Jared and Connie scored the same number of points, so Connie's score is also JJ. Bryan scored twice as many as Connie, so Bryan's score is 2J2J. The total points scored by the team is 8686. We can set up an equation to represent this information:\newlineJ2\frac{J}{2} (Josiah) + JJ (Jared) + (J−2)(J - 2) (Maricella) + JJ (Connie) + 2J2J (Bryan) = 8686
  2. Simplify Equation: Combine like terms to simplify the equation:\newlineJ2+J+J−2+J+2J=86\frac{J}{2} + J + J - 2 + J + 2J = 86\newlineThis simplifies to:\newline5.5J−2=865.5J - 2 = 86
  3. Isolate Terms with J: Add 22 to both sides of the equation to isolate the terms with J:\newline5.5J−2+2=86+25.5J - 2 + 2 = 86 + 2\newline5.5J=885.5J = 88
  4. Solve for J: Divide both sides by 5.55.5 to solve for JJ: \newline5.5J5.5=885.5\frac{5.5J}{5.5} = \frac{88}{5.5}\newlineJ=16J = 16
  5. Find Player Scores: Now that we have the value for JJ, we can find the scores for each player:\newlineJosiah's score is J2=162=8\frac{J}{2} = \frac{16}{2} = 8\newlineMaricella's score is J−2=16−2=14J - 2 = 16 - 2 = 14\newlineConnie's score is J=16J = 16\newlineBryan's score is 2J=2×16=322J = 2 \times 16 = 32

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