Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks. $\newline$ Jordan and Donald went to an arcade where the machines took tokens. Jordan played $1$ game of skee ball and $7$ games of pinball, using a total of $23$ tokens. At the same time, Donald played $2$ games of skee ball and $3$ games of pinball, using up $13$ tokens. How many tokens does each game require? $\newline$ Every game of skee ball requires $\_$ tokens, and every game of pinball requires $\_$ tokens.

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Solve a system of equations using elimination: word problems

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

\newline

Jordan and Donald went to an arcade where the machines took tokens. Jordan played

1

game of skee ball and

7

games of pinball, using a total of

23

tokens. At the same time, Donald played

2

games of skee ball and

3

games of pinball, using up

13

tokens. How many tokens does each game require?

\newline

Every game of skee ball requires

\_

tokens, and every game of pinball requires

\_

tokens.

Denote Tokens for Games: Let's denote the number of tokens required for a game of skee ball as $s$ and for a game of pinball as $p$ . Jordan played $1$ game of skee ball and $7$ games of pinball, using a total of $23$ tokens. This gives us the equation $s + 7p = 23$ .
Jordan's Games and Tokens: Donald played $2$ games of skee ball and $3$ games of pinball, using up $13$ tokens. This gives us the equation $2s + 3p = 13$ .
Eliminate Variable $s$ : We now have a system of two equations. We need to eliminate one of the variables, $s$ or $p$ . We choose to eliminate $s$ because its coefficients are $1$ and $2$ , which are easier to work with.
Multiply and Subtract Equations: To eliminate $s$ , we multiply the first equation by $2$ , the coefficient of $s$ in the second equation. This gives us the new equation $2s + 14p = 46$ .
Solve for $p$ : We now subtract the second equation from the new first equation to eliminate $s$ . This gives us $11p = 33$ .
Substitute $p$ into Equation: Solving for $p$ , we divide both sides of the equation by $11$ , which gives us $p = 3$ .
Final Solution: We substitute $p = 3$ into the first equation and solve for $s$ . This gives us $s + 7(3) = 23$ , which simplifies to $s + 21 = 23$ .
Final Solution: We substitute $p = 3$ into the first equation and solve for $s$ . This gives us $s + 7(3) = 23$ , which simplifies to $s + 21 = 23$ . Subtracting $21$ from both sides of the equation, we get $s = 23 - 21$ , which gives us $s = 2$ .