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Solving Equations in Real-World Scenarios: Homework Problems

This homework assignment presents a series of engaging mathematical problems involving equations. A student is tasked with determining the change from purchases of pens and pencils, calculating the composition of a nut mixture sold at a grocery store, solving a point-loss game at an amusement park, and figuring out the mixture of poison solutions for an insecticide. Each problem involves defining variables and writing equations to solve for unknown quantities, enhancing problem-solving skills.

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Solving Equations in Real-World Scenarios: Homework Problems

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  1. Homework If you buy six pens and one mechanical pencil, you’ll get only $1 change from your $10 bill. But if you buy four pens and two mechanical pencils, you’ll get $2 change. How much change would you get back from your $10 bill if you bought just one pen and one pencil? #1 Define variables: Write two equations p= cost pen m= cost of a mech. pencil

  2. Homework A grocery store mixes together some cashews costing $8 per pound with some Brazilian nuts costing $10 per pound. The store sold 12 pounds of the mixture for $8.50 per pound. How many pounds of cashews were in the mixture the store sold? #2 C= amount of cashews (lbs.). 8.50(12) = 102 B= amount of Brazils (lbs.) + = Mixture Brazil Cashews B 12 C Amount (lbs) 102 10B 8C Cost ($)

  3. Homework A grocery store mixes together some cashews costing $8 per pound with some Brazilian nuts costing $10 per pound. The store sold 12 pounds of the mixture for $8.50 per pound. How many pounds of cashews were in the mixture the store sold? #2 C= amount of cashews (lbs.). B= amount of Brazils (lbs.) 9 pounds of cashews

  4. Homework At an amusement park there’s a game where you get 5 points for each bull’s eye you hit, but you lose 10 points for every miss. Jack played the game and after 30 tries he had lost 90 points. How many bull’s eyes did he make? #3 Define variables: Write two equations B= number of Bull’s eyes M= number of Misses 14 Bull’s eyes

  5. Homework A chemist wants to make 60 liters of a powerful insecticide spray that is 30% poison. He plans on mixing a 80% poison solution into a 20% poison solution. How much of each solution will he need to make his insecticide? #4 a= amount of 20% poison 0.30(60) = 18 b= amount of 80% poison + 30% 20% 80% = Amount of poison a b 60 18 0.20a 0.80b Pure poison

  6. Homework A chemist wants to make 60 liters of a powerful insecticide spray that is 30% poison. He plans on mixing a 80% poison solution into a 20% poison solution. How much of each solution will he need to make his insecticide? #4 a= amount of 20% poison b= amount of 80% poison 50 liters of 20% poison 10 liters of 80% poison

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