1. **State the problem:** We need to find the cost of each game: racing game ($r$), pinball ($p$), and air hockey ($a$) given the total amounts spent by Marcos, Sara, and Darius. 2. **Set up the system of equations:** - Marcos: $6r + 2p + 1a = 6$ - Sara: $3r + 4p + 5a = 12$ - Darius: $2r + 7p + 4a = 12.25$ 3. **Solve the system:** From Marcos' equation: $$a = 6 - 6r - 2p$$ Substitute $a$ into Sara's and Darius' equations: - Sara: $3r + 4p + 5(6 - 6r - 2p) = 12$ - Darius: $2r + 7p + 4(6 - 6r - 2p) = 12.25$ 4. **Simplify Sara's equation:** $$3r + 4p + 30 - 30r - 10p = 12$$ $$3r - 30r + 4p - 10p + 30 = 12$$ $$-27r - 6p + 30 = 12$$ $$-27r - 6p = 12 - 30$$ $$-27r - 6p = -18$$ 5. **Simplify Darius' equation:** $$2r + 7p + 24 - 24r - 8p = 12.25$$ $$2r - 24r + 7p - 8p + 24 = 12.25$$ $$-22r - p + 24 = 12.25$$ $$-22r - p = 12.25 - 24$$ $$-22r - p = -11.75$$ 6. **Rewrite the system:** $$\begin{cases} -27r - 6p = -18 \\ -22r - p = -11.75 \end{cases}$$ 7. **Solve for $p$ from second equation:** $$-22r - p = -11.75$$ $$p = -22r + 11.75$$ 8. **Substitute $p$ into first equation:** $$-27r - 6(-22r + 11.75) = -18$$ $$-27r + 132r - 70.5 = -18$$ $$105r - 70.5 = -18$$ $$105r = -18 + 70.5$$ $$105r = 52.5$$ $$r = \frac{52.5}{105} = 0.5$$ 9. **Find $p$:** $$p = -22(0.5) + 11.75 = -11 + 11.75 = 0.75$$ 10. **Find $a$ using Marcos' equation:** $$a = 6 - 6(0.5) - 2(0.75) = 6 - 3 - 1.5 = 1.5$$ **Final answer:** - Racing game: $0.5$ - Pinball: $0.75$ - Air hockey: $1.5$