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Solving Linear Equations with Combinations: Real-Life Applications

This guide explores practical problems involving linear equations and their solutions through linear combinations. It includes scenarios like museum admissions, office supply sales, high school play ticket sales, and softball orders. Each example provides a real-world context, with specific prices and totals, to illustrate how to set up and solve systems of linear equations. By applying this method, you will learn how to determine quantities from combined totals efficiently, enhancing your problem-solving skills.

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Solving Linear Equations with Combinations: Real-Life Applications

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  1. Systems of Linear Equations

  2. Solve

  3. Solve using linear combinations. In one day a museum collected $1590 from 321 people admitted to the museum. The price of each adult admission is $6 and each child admission is $4. Estimate how many adults and how many children were admitted that day.

  4. Solve using linear combinations. An office supply company sells two types of fax machines. They charge $150 for one of the machines and $225 for the other. If the company sold 22 fax machines for a total of $3900 last month, how many of each type were sold?

  5. Solve using linear combinations. You are selling tickets for a high school play. Student tickets cost $4 and general admission tickets cost $6. You sell 525 tickets and collect $2876. How many of each type of ticket did you sell?

  6. Solve using linear combinations. You are ordering softballs for two softball leagues. The Pony League uses an 11-inch softball priced at $2.75. The Junior League uses a 12-inch softball priced at $3.25. The bill smeared in the rain, but you know the total was 80 softballs for $245. How many of each size did you order?

  7. Solve using linear combinations.

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