solve systems of equations substitution 2

Poll

How are you feeling today?

Open Ended

If your team wanted to try building something like this, what would you need to know?

​Let's say you have $1,000 to spend. (not much really). You have 2500 square feet to work with.

You think you would like to purchase some modules, each module has a specific size and cost.

Module A costs $200 per module and takes up 25 square feet

Module B costs $150 per module and takes up 50 square feet

​Let's say you have $1,000 to spend. (not much really). You have 2500 square feet to work with.

You think you would like to purchase some modules, each module has a specific size and cost.

Module A costs $200 per module and takes up 25 square feet

Module B costs $150 per module and takes up 50 square feet

​Let's look at the cost of each first and assume we will spend exactly $1000 (because we don't feel like dealing with inequalities yet)

Multiple Choice

Let's look at cost first and assume we will spend exactly $1000

Module A costs $200 per module

Module B costs $150 per module

Which equation represents this situation?

• 200A + 1000

  = B

• 200A + 150B

  = 1000

• A + B =

  1000

• 150B + 1000

  = A

Multiple Choice

Next, consider the space constraints

You have 2500 square feet to work with.

Module A takes up 25 square feet

Module B takes up 50 square feet

Which equation represents this constraint?

• 25A + 50B

  =2500

• 25A - 50B

  = 2500

• 2500 + 50B

  = 25A

• A + B

  =2500

​We now have a system of equations

​200A +150B = 1000

25A + 50B = 2500

Poll

Given this system of equations:

200A + 150B = 1000

25A +50B = 2500

Where would you like to start?

• Solve for A in the first equation

• Solve for A in the second equation

• Solve for B in the first equation

• Solve for B in the first equation

​200A + 150B = 1000

25A +50B = 2500

​you wanted to . . .

​200A + 150B = 1000

25A +50B = 2500

​Substitute into the other equation

​200A + 150B = 1000

25A +50B = 2500

​Solve for the chosen variable

​200A + 150B = 1000

25A +50B = 2500

​Solve for the other variable

​Let's say you have $1,000 to spend. (not much really). You have 2500 square feet to work with.

You think you would like to purchase some modules, each module has a specific size and cost.

Module A costs $200 per module and takes up 25 square feet

Module B costs $150 per module and takes up 50 square feet

​Answer the question in the context of the problem. We found that to spend exactly $1000 and use exactly 2500 square space you will need 88 A modules and 6 B modules.

Poll

If you needed to pay 10% sales tax and can't exceed $1000, what would you do?

• Buy one less of module A

• Buy one less of module B

• Depends on how cool each module is

• See what my team likes best

​Real problems get more complicated with multiple variables and constraints. Practice with the smaller ones to become comfortable with the bigger puzzles.

one last Rube before you go to practice