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Fabio and Carlos play on a basketball team together. In the last game, Fabio had 7 points less than 2 times as many points as Carlos. Fabio scored 31 points in the game. How many points did Carlos score in the last game?

Fabio and Carlos play on a basketball team together. In the last game, Fabio had $7$ points less than $2$ times as many points as Carlos. Fabio scored $31$ points in the game. How many points did Carlos score in the last game?

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Solve proportions: word problems

Full solution

Q. Fabio and Carlos play on a basketball team together. In the last game, Fabio had

7

points less than

2

times as many points as Carlos. Fabio scored

31

points in the game. How many points did Carlos score in the last game?

Denote Carlos' Points: Let's denote Carlos' points as $C$ . According to the problem, Fabio scored $7$ points less than twice as many points as Carlos. This can be written as an equation: $\newline$ Fabio's points $= 2 \times C - 7$ $\newline$ We know Fabio scored $31$ points, so we can substitute this into the equation: $\newline$ $31 = 2 \times C - 7$
Equation for Fabio's Points: Now, we need to solve for $C$ . First, we add $7$ to both sides of the equation to isolate the term with $C$ on one side: $\newline$ $31 + 7 = 2 \times C - 7 + 7$ $\newline$ $38 = 2 \times C$
Solve for C: Next, we divide both sides of the equation by $2$ to solve for C: $\newline$ $\frac{38}{2} = \frac{2 \times C}{2}$ $\newline$ $19 = C$
Carlos' Points Calculation: We have found that Carlos scored $19$ points in the last game.

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