Skill 5 Intro Lesson

Get out your packet

​Go to page 17!

Instructions: On your notes, write down anything written in RED

Page 17 - Problem 1

Loudon Swain scored an incredible 30 points at the state wrestling meet by only receving points for takedowns (2 points) and escapes (1 point). Define variables, write an equation.

​Write down an equation in this format: __x +__y = ___

Discuss with your neighbor and check your equation on the next slide!

Page 17 - Problem 1

Loudon Swain scored an incredible 30 points at the state wrestling meet by only receving points for takedowns (2 points) and escapes (1 point). Define variables, write an equation.

​This equation would be: 2x + 1y = 30

Where x = # of takedowns, y = # of escapes

Page 17 - Problem 2

On a final exam in Am. History, you can earn 2 points for every correct mult. choice and 5 points for every essay question. Alex Ham scored 95 points total on his final.

​Write down an equation in this format: __x +__y = ___

Discuss with your neighbor and check your equation on the next slide!

Page 17 - Problem 2

On a final exam in Am. History, you can earn 2 points for every correct mult. choice and 5 points for every essay question. Alex Ham scored 95 points total on his final.

This equation would be: 2x + 5y = 95

Where x = # of multiple choice correct, y = # of essay correct

Page 17 - Problem 3

Salesman Dan traveled from Council Bluffs to Richmond. He traveled by car going 60 mph and then by train going 80 mph. He traveled a total of 900 miles.

​Write down an equation in this format: __x +__y = ___

Discuss with your neighbor and check your equation on the next slide!

Page 17 - Problem 3

Salesman Dan traveled from Council Bluffs to Richmond. He traveled by car going 60 mph and then by train for 80 mph. He traveled a total of 900 miles.

​The equation would be: 60x + 80y = 900

Where x = # of hours in a car, y = # of hours in a train

Multiple Choice

Jenny went to the sale at Kohl's last weekend.  
T-shirts were on sale for $15 each and hoodies were on sale for $20 each.  If she spent $150 total, write an equation to represent this situation.  

• 20x + 15 = y 
• 35x = y 
• 15x + 20y = 150 
• 150 - 20x = 15y 

Drag and Drop

Fill in the blanks to write the equation:

​

Placeholder

x + ​

Placeholder

y = ​

Placeholder

Drag these tiles and drop them in the correct blank above

2

5

60

7

53

5/2

2/5

Fill in the Blanks

Write the equation for the situation:

Multiple Choice

This graph shows the number of bird houses Nyla can make with her 80 feet of material. What is the meaning of the point (4,12)

• She can make 4 small houses and 12 large houses

• She can make 4 Large houses and 12 small houses

• She can only make 4 large houses

• She can only make 12 small houses

Multiple Choice

Here are both graphs. At what point do these two lines cross?

• (3,4)

• (4,3)

• (-3,4)

• (-4,3)

• (3,-4)

Flip your packet to page 18.

Try to answer questions #1-4 based on the situation/equations about candy

Open a new tab and open
desmos.com/calculator

Type in the two equations from the candy problem so it looks like this:

The graph looks like this:

​#4:
The solution is
x= 1.75 and y =1.25 because that is where they intersect.

This means 1.75 pounds of caramels (because caramels was x) and 1.25 pounds of truffles (because truffles were y)

Page 18

All 30 students in the class are buying a calculator. Some are buying a scientific calculator while others are buying graphing calculators. Each scientific is $15 and each graphing is $80. The class spent a total of $1750.

​Write down TWO equations in this format:
__x +__y = ___
__x +__y = ___

Discuss with your neighbor and check your equations on the next slide!

Page 18

All 30 students in the class are buying a calculator. Some are buying a scientific calculator while others are buying graphing calculators. Each scientific is $15 and each graphing is $80. The class spent a total of $1750.

​15x+80y = 1750 <-- This equation represents the money spent/total

x + y = 30 <---- This equation represents that the total number of calculators needs to be 30

x = # of scientific calcs
y = # of graphing calcs

Page 18

All 30 students in the class are buying a calculator. Some are buying a scientific calculator while others are buying graphing calculators. Each scientific is $15 and each graphing is $80. The class spent a total of $1750.

​15x+80y = 1750

x + y = 30

x = # of scientific calcs
y = # of graphing calcs

​Type both equations into desmos.com/calculator in another tab.


What is the point of solution?

(___,___)

Multiple Choice

What is the solution you got from graphing these equations on Desmos?

• 10 scientific and 20 graphing

• 20 scientific and 10 graphing

• 15 and 80

• 30 of each calculator

Multiple Choice

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6
• x + y = 4
  x - y = 6
• 4x + 6y = 13
  3x + 7y = 13.5
• 4x - 6y = 13
  3x - 7y = 13.5

Multiple Choice

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

Multiple Choice

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Which system of equations represents the situation?

• x + y = 15
  4x + 2y = 44
• 4x + 2y = 15
  x + y = 44
• x = 2y + 44
  4x = y + 15
• 2x - 4y = 44
  x - y = 15

Multiple Choice

Jon has a total of 25 quarters and dimes.  The amount of money he has is $5.65.  Which system models this scenario?

• Q + D = 25
  .25Q + .10D = 5.65
• Q + D = 5.65
  .25Q + .10D = 25
• .25Q + .10D = 25
  Q + D = 5.65