More About Equations
Presentation
•
Mathematics
•
9th - 12th Grade
•
Hard
+12
Standards-aligned
Laura Wroten
FREE Resource
12 Slides • 21 Questions
1
More about equations
By Laura Wroten
2
n - number she is thinking of
6 less than means something minus 6
product of 7 and this number means 7n
is 85 means equals 85
so, 7n-6 = 85 is the equation
How do we start this?
3
Multiple Choice
1
2
3
4
4
How to write a linear equation from a table:
OR... put each equation in y= in the calculator and find the one with a table that matches.
DO NOT GUESS!!!!!!!!
5
Multiple Choice
Which answer was correct on the previous slide?
a
b
c
d
6
Product of a number and 3
3n
Increased by 5
3n +5
is
3n+5 =
7 less than
3n+5= ?-7
twice the number
3n+5 = 2n-7
Read carefully!
7
Multiple Choice
1
2
3
4
8
Set the two situations equal to each other and solve!
*Also, you can't add feet and inches, so I'm going to change everything to inches in my equation
3x12 = 36 and 4x12 = 48
36+ 15x (Type A)
48 + 10x (Type B)
Solve: 36 + 15x = 48 + 10x
Key words = SAME height
DESMOS Tip of the Day
If you have an equation with a variable on both sides, put it in Desmos like this
y=36+15x
y=48+10x
Look for the x value of the point where the two lines cross
DO NOT GUESS!!!!
9
Multiple Choice
-5 years
2.4 years
7.2 years
72 years
10
Fill in the Blanks
Type answer...
11
Practice problems
Use your resources, but DO NOT JUST GUESS!
12
Explanation Slide...
The correct equation is C = 2h + 15, which represents the total cost C to rent the boat for h hours with a $15 deposit fee and $2 per hour charge.
13
Multiple Choice
Speedy Boat Rental charges a $15 deposit fee plus $2 for each hour of use to rent a paddle boat. Write an equation for C, the total cost, to rent the boat for h hours.
h = 2C + 15
C = 15h + 2
h = 15C + 2
C = 2h + 15
14
Explanation Slide...
The correct equation in slope-intercept form is y = 5x + 20 because the $20 startup fee is the y-intercept (20) and the $5 monthly fee represents the slope (5).
15
Multiple Choice
In order to join an online learning community, there is a $20 startup fee and a $5 monthly fee. Write an equation in slope-intercept form that models this situation.
y = 20x + 5
y = 5x +20
16
Explanation Slide...
Dexter paid $8.90 for his hamburger, which means he got 5 toppings as each topping costs $1.78 (8.90 / 1.78 = 5). Therefore, Dexter got 5 toppings.
17
Multiple Choice
If Dexter pays $8.90 for his hamburger, how many toppings did he get?
3
4
5
6
18
Explanation Slide...
The initial fee of $25.
19
Multiple Choice
A T-shirt design company charges your team an initial fee of $25 to create the team's design. Each t-shirt printed with your design costs an additional $8. The equation for this situation is y = 8x + 25. Interpret the y-intercept in context.
The additional fee of $8.
The initial fee of $25.
The additional fee of $25.
The initial fee of $8.
20
Multiple Choice
When 4 people attend the movie theater, it costs $23.96. When 7 people attend the movie theater, it costs $41.93. What information is given and which equation should you use?
A slope and y - intercept are given, use y = mx + b.
A slope and y - intercept are given, use y - y1 = m(x - x1).
Two points are given; use y - y1 = m(x - x1).
Two different items that add to a total are given; use Ax + By = C.
21
Multiple Choice
You and your friends go to the movies and purchase some popcorn and Pepsi. Popcorn is sold for $4.99 per bag and Pepsi is sold for $1.99 per bottle. You each chip in to pay $24.92. Write an equation to represent the given situation.
y = 1.99x + 4.99
y = 4.99x + 24.92
y - 1.99 = 4.99(x - 24.92)
1.99x + 4.99y = 24.92
22
Multiple Choice
23
Multiple Choice
24
Multiple Choice
25
Multiple Choice
26
They aren't usually multiple choice like this so you have to know how to set them up and work them out.
If the first term is n, then you have to add 2 each time to keep every number odd.
n + n+2 + n+4 = 93 which simplifies to 3n+6 = 93
Since n is 29, then n+2 is 31 and n+4 is 33
Do you remember consecutive integer questions?
27
Multiple Choice
What is the correct answer from the previous slide?
A
B
C
D
28
Multiple Choice
Three brothers have ages that are consecutive integers. Together, their ages have a sum of 75. What is the middle brother's age?
n + n+1 + n+2 = 75
(We only add one more each time because it's not even or odd - just consecutive.)
23
24
25
26
29
Multiple Choice
The last three days' temperatures have been consecutive even numbers that add up to a sum of -12. Which of these numbers was NOT a temperature over the last 3 days?
-6
-4
-2
0
30
What about time and work problems?
31
Fill in the Blanks
Type answer...
32
Fill in the Blanks
Type answer...
33
Fill in the Blanks
Type answer...
More about equations
By Laura Wroten
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