Model and Write Equations and Inequalities

The equation C = 50 + 1.25 (x – 100) models the yearly cost, C, to use a professional photo printing service.  To use the service, Jessica pays a $50 yearly subscription fee and $1.25 per photo after the first 100 photos (the first 100 photos are included with the $50 subscription).   The variable x represents the number of photographs.   Rewrite the formula for x in terms of C. 

An automobile dealership sells Model A cars and Model B trucks.  The matrix equation models a system of linear equations that relates the revenue generated from the sale of the vehicles and the number of (Model A) cars and (Model B) trucks sold in the month of April.   

In the next month, the dealership sold twice as many cars and half as many trucks.  Did the dealership make more or less money in May than in April?

• The dealership made more money in May than April.

• The dealership made less money in May than April.

• Impossible to know. Need more information.

There are 50 donkeys and chickens on a farm.  There are a total of 174 legs.  Which system below can be used to figure out how many of each animal the farm has?

• d + c = 174
  4d + 2c = 50

• d + c = 50
  4d + 2c = 174

• d + c = 50
  2d + 4c = 174

• d + c = 174
  2d + 4c = 50

Use substitution to solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

Your family goes to a southern style restaurant for dinner. There are 6 total people in your family. Some order chicken for $14 and the rest order steak for $17. The total bill is $99. Write a system that could represent this situation.

• c + s = 6
  14c + 17s = 99

• c + s = 99
  14c + 17s = 6

• c + s = 6
  17c + 14s = 99

• c + s = 99
  17c + 14s = 6

Solve using substitution.
x - 2y = 2
3x + 4y = 3

• (1.4, -0.3)

• (3.1, 5)

• (-2.5, 3.5)

• (6.9, 1.02)

Match: the overlap is on the left!

• y ≤ 3x   and  y ≤ -2x + 4

• y > 3x   and  y > -2x + 4

• y < 3x   and  y > -2x + 4

• y > 3x   and  y < -2x + 4

Select the correct graph for each inequality.

• A

• B

• C

• D

• y < x−2 
  y < 3
• y > -x+2
  y > 3
• y < -x+2
  y < 3
• y < -x+2
  y > 3