Subjects algebra

Symbol Equations 904Ebe

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1. **State the problem:** We have a system of equations with symbols representing unknown values: $$\text{pirate} + \text{pirate} + \text{squid} = 21$$ $$\text{anchor} + \text{map} + \text{anchor} = 13$$ $$\text{map} + \text{map} = 6$$ $$\text{anchor} + \text{ship} = 9$$ $$\text{pirate} + \text{ship} = 14$$ We want to find the value of: $$\text{squid} + \text{pirate} + \text{map} + \text{ship}$$ 2. **Assign variables:** Let $$p = \text{pirate},\quad s = \text{squid},\quad a = \text{anchor},\quad m = \text{map},\quad sh = \text{ship}$$ 3. **Rewrite equations:** $$2p + s = 21$$ $$2a + m = 13$$ $$2m = 6$$ $$a + sh = 9$$ $$p + sh = 14$$ 4. **Solve for $m$ from third equation:** $$2m = 6 \implies m = \cancel{\frac{2m}{2}}{\frac{6}{2}} = 3$$ 5. **Substitute $m=3$ into second equation:** $$2a + 3 = 13 \implies 2a = 13 - 3 = 10 \implies a = \cancel{\frac{2a}{2}}{\frac{10}{2}} = 5$$ 6. **Use $a=5$ in fourth equation to find $sh$:** $$5 + sh = 9 \implies sh = 9 - 5 = 4$$ 7. **Use $sh=4$ in fifth equation to find $p$:** $$p + 4 = 14 \implies p = 14 - 4 = 10$$ 8. **Use $p=10$ in first equation to find $s$:** $$2(10) + s = 21 \implies 20 + s = 21 \implies s = 21 - 20 = 1$$ 9. **Calculate the final sum:** $$s + p + m + sh = 1 + 10 + 3 + 4 = 18$$ **Final answer:** $$\boxed{18}$$