Algebra

# System of Linear Equations Word Problems

Calvin went to Chicago's Magnificent Mile to do some Christmas shopping. At the first store, he bought some t-shirts and spent half of his money. At the second store, he bought a stuffed bear and spent half of his remaining money. For lunch, he bought a sandwich for half of his remaining money. He then had $10 left to take the train home. How much money did Calvin bring along at the start of the day? A group of friends are planning a road trip. If they all contribute$24, then they would be $6 short of the total cost of the trip. If they all contribute$25, then they would have $3 more than the total cost of the trip. What is the total cost of the trip? Stella the school teacher is bringing 38 of her students out on a field trip. The bus that contains her students has 25 rows of seats, and each row contains 2 seats. When taking attendance on the bus, she notices there was no empty row of seats. How many rows of seats have exactly 1 student in them? Susan's backyard has three faucets: $$A$$, $$B$$ and $$C$$. If she turns on all three of them, it takes $$100$$ minutes to fill the pool. If she turns on only $$A$$ and $$B$$, it takes $$150$$ minutes, and if she turns on only $$B$$ and $$C$$, it takes $$200$$ minutes. If she turns on only $$A$$ and $$C$$, how long will it take (in minutes) to fill the pool? A candy store sells almonds for$$$15$$ per kilogram and peanuts for $$$5$$ per kilogram. If it sells $$20$$ kilograms of mixed nuts for$$$13$$ per kilogram, how many kilograms of almonds are in the mixed nuts?

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