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

Question

Emilia and Cooper went to an arcade where the machines took tokens. Emilia played 7 games of skee ball and 10 games of pinball, using a total of 47 tokens. At the same time, Cooper played 9 games of skee ball and 9 games of pinball, using up 45 tokens. How many tokens does each game require?

Every game of skee ball requires
tokens, and every game of pinball requires
tokens.

Answer 1

Let \( x \) be the number of tokens required for each game of skee ball, and let \( y \) be the number of tokens required for each game of pinball.

We can set up the following system of equations based on the information given:

1. For Emilia's games: \[ 7x + 10y = 47 \]
2. For Cooper's games: \[ 9x + 9y = 45 \]

Now we will solve this system of equations.

Step 1: Simplify the second equation

The second equation can be simplified by dividing all terms by 9: \[ x + y = 5 \]

Step 2: Substitute

Now we can express \( y \) in terms of \( x \): \[ y = 5 - x \]

Step 3: Substitute into the first equation

Substituting \( y \) into the first equation: \[ 7x + 10(5 - x) = 47 \]

Step 4: Distribute and solve for \( x \)

\[ 7x + 50 - 10x = 47 \] Combine like terms: \[ -3x + 50 = 47 \] Subtract 50 from both sides: \[ -3x = -3 \] Divide by -3: \[ x = 1 \]

Step 5: Solve for \( y \)

Now substitute \( x = 1 \) back into the equation \( y = 5 - x \): \[ y = 5 - 1 = 4 \]

Conclusion

We have found that:

• Every game of skee ball requires \( 1 \) token.
• Every game of pinball requires \( 4 \) tokens.

So the final answers are: Every game of skee ball requires 1 token, and every game of pinball requires 4 tokens.