Linear Applications: Standard Form

Read the problem carefully. Define the variables. Write the equation in standard form. Solve for the x-intercept by substituting in zero for y. Solve for the y-intercept by substituting in zero for x. Plot the intercepts. Graph the line. Answer the problem.

The student government is sponsoring a pancake dinner to raise money for a field trip. The officers estimate that 200 adults and 300 children will attend. Write an equation, graph the line, and determine reasonable ticket prices to set in order to raise $4200.

The student government is sponsoring a pancake dinner to raise money for a field trip. The officers estimate that 200 adults and 300 children will attend. Write an equation, graph the line, and determine reasonable ticket prices to set in order to raise $4200. Step 1: Read the problem carefully. Step 2: Define the variables. Let x = cost of an adult ticket Let y = cost of a student ticket Step 3: Write the equation in standard form. 200x + 300y = 4200

Step 4: Solve for the x-intercept by substituting in zero for y. 200x + 300(0) = x = 4200 x = 21 Step 5: Solve for the y-intercept by substituting in zero for x. 200(0) + 300y = y = 4200 x = 14 So the x intercept is (21,0) and the y intercept is (0, 14).

Step 6: Plot the intercepts. Step 7: Graph the line. Step 8: Answer the question. What are reasonable ticket prices?

You are running a concession stand at the basketball game. You sell hot dogs for $1 and sodas for $0.50. At the end of the night, you made $200. Write an equation, graph the line, and determine the possible number of hot dogs and sodas that were sold.

You are running a concession stand at the basketball game. You sell hot dogs for $1 and sodas for $0.50. At the end of the night, you made $200. Write an equation, graph the line, and determine the possible number of hot dogs and sodas that were sold. Step 1: Read the problem carefully. Step 2: Define the variables. Let x = # of hot dogs sold Let y = # of sodas sold Step 3: Write the equation in standard form. 1x y = 200

Step 4: Solve for the x-intercept by substituting in zero for y. 1x (0) = 200 1x = 200 x = 200 Step 5: Solve for the y-intercept by substituting in zero for x. 1(0) y = y = 200 y = 400 So the x intercept is (200,0) and the y intercept is (0, 400).

Step 6: Plot the intercepts. Step 7: Graph the line. Step 8: Answer the question. What combination of hot dogs/sodas could have been sold?