Using Standard Form in Real World Context

Example

• A 100-point test has 2 point questions, and 4 points questions. Write an equation in standard form relating the number of questions. Use x to represent the 2 point questions and y to represent the 4 point questions.

2x + 4y = 100

• If there are 10 questions worth 4 points, how many questions are worth 2 points? 2x + 4(10) = 100

• Louise has $60 in five-dollar bills and singles. Write an equation in standard form relating the number of $5 bills and $1 bills. Use x to represent the $5 and y to represent the $1.

• If she has nine $5 bills, how many $1 bills does she have?

The Rammy family bought 4 sandwiches and 3 salads. They spent $36. Write an equation in standard form relating the cost of the items. Let x be the cost of a sandwich and y be the cost of a salad.

If the cost of a sandwich is $6, how much are each of the salads?

• The store at which Andy usually shops is having a sale. Roast beef costs $4 a pound and shrimp costs $10 a pound. Write an equation to describe different possible combinations of Roast beef and shrimp that he can buy for $96 using x to represent pounds of roast beef and y to represent pounds of shrimp.

• If Andy purchased 7 pounds of shrimp, how much roast beef did he buy?

• The Plano Texans are a youth marching band that competes with other groups all over the country. The band director rents instruments to members. Each trumpet rents for $10 per month and each drum rents for $5 per month. Write an equation that relates the trumpet and drum rentals if the band director collected $115 in rental fees.

• If 16 drums were rented, how many trumpets were rented?