Equations in Standard Form: Real-World Applications

A school is planning to build a new playground. The length of the playground is 20 meters more than twice the width. Write an equation in standard form that represents this relationship.

• l - 2w = 20

• l = 2w + 10

• 2w - l + 20 = 0

• l + 20 = 2w

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an equation in standard form to represent the total cost (C) based on the number of miles (m) driven.

• C = 0.20m - 50

• 0.20m - C = -50

• C = 50m + 0.20

• C = 50 + 0.20m

A local bakery sells cupcakes for $2 each and cookies for $1 each. If the total sales for the day were $150, write an equation in standard form to represent the relationship between the number of cupcakes (c) and cookies (k) sold.

• 2c + 3k = 150

• 3c + k = 150

• c + 2k = 150

• 2c + k = 150

A concert hall has a seating arrangement where the number of rows (r) is 5 less than twice the number of seats per row (s). Write the equation in standard form that represents this relationship.

• 2r - s = 5

• 2s - r = 5

• r + 5 = 2s

• r = 2s + 5

Convert the equation 2x + 3y = 12 into standard form. What are the coefficients of x and y?

• Coefficients: x = 1, y = 4

• Coefficients: x = 3, y = 2

• Coefficients: x = 0, y = 5

• Coefficients: x = 2, y = 3

Identify the standard form of the equation 4x - 2y = 8. What are the values of A, B, and C in the standard form Ax + By = C?

• A = 8, B = -2, C = 4

• A = 4, B = -2, C = 8

• A = 4, B = 2, C = 8

• A = 2, B = -4, C = 8

A store sells pencils for $0.50 each and erasers for $0.75 each. If a student buys a total of 10 items and spends $6.00, write an equation in standard form to represent the relationship between the number of pencils (p) and erasers (e) bought.

• 20p + 80e = 600

• 25p + 50e = 600

• 10p + 75e = 600

• 25p + 75e = 600

A swimming pool is being designed to be 10 meters longer than it is wide. If the width is represented by w, write the equation in standard form that represents the dimensions of the pool.

• x + y = 10w

• x - y = -10

• x - y = 0

• x + y = 10

Convert the equation 3x - 4y = 24 into standard form. What is the value of C when the equation is expressed as Ax + By = C?

• 20

• 30

• 24

• 15