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In a game, you will score $20$ points if you win but will have $5$ points deducted if you lose. Ken played $35$ games and scored $475$ points. How many games did he win?

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Add and subtract whole numbers: word problems

Full solution

Q. In a game, you will score

20

points if you win but will have

5

points deducted if you lose. Ken played

35

games and scored

475

points. How many games did he win?

Define Equations: Let's denote the number of games Ken won as $W$ and the number of games he lost as $L$ . We know that Ken played a total of $35$ games, so $W + L = 35$ . This is our first equation.
Total Points Equation: We also know that Ken scored $475$ points. For each game won, he scores $20$ points, and for each game lost, he loses $5$ points. So, the total points can be represented by the equation $20W - 5L = 475$ . This is our second equation.
Elimination Method: Now we have a system of two equations: $\newline$ $1$ ) $W + L = 35$ $\newline$ $2$ ) $20W - 5L = 475$ $\newline$ We can solve this system using the substitution or elimination method. Let's use the elimination method by multiplying the first equation by $5$ to align the $L$ terms.
Add Equations: Multiplying the first equation by $5$ gives us $5W + 5L = 175$ . Now we have: $\newline$ $1$ ) $5W + 5L = 175$ $\newline$ $2$ ) $20W - 5L = 475$ $\newline$ We can add these two equations to eliminate $L$ .
Solve for W: Adding the two equations gives us: $\newline$ $5W + 5L + 20W - 5L = 175 + 475$ $\newline$ This simplifies to: $\newline$ $25W = 650$ $\newline$ Now we can solve for W by dividing both sides by $25$ .
Final Result: Dividing both sides by $25$ gives us: $\newline$ $W = \frac{650}{25}$ $\newline$ $W = 26$ $\newline$ So, Ken won $26$ games.

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