Students:
Adults:
$5(100) = $500
$10(50) = $500
Total amount of money is $500 + $500 = $1000.
They would collect $1375.
They would
collect $1645.
1) Find the amount of money collected from students by
multiplying the cost per student by the number of student tickets
sold.
2) Find the amount of money collected from adults by multiplying
the cost per adult by the number of adult tickets sold.
3) Then add the amounts together to find the total amount of
money collected!
5s + 10a
5s represents the total amount of
money collect from students.
10a represents the total amount of
money collected from adults.
5s + 10a represents the amounts
added together to find the total
amount of money collected.
No!
You need to also know the number of adult tickets sold
to find the total amount of money collected.
No!
The number of student tickets and adult tickets are independent
of each other and the total amount of money collected is
dependent on both the student and adult tickets sold.
5s + 10a = 3000
The equation has a fixed amount of $3000.
#1
#2
#3
#4
Student
Tickets
Sold
Adult
Tickets
Sold
Money
from
students
Money
from
adults
Total
money
collected
tickets
tickets
dollars
dollars
dollars
175
1250
1750
3000
5s + 10a = 3000
5(95) + 10a = 3000
475 + 10a = 3000
-475
-475
10a = 2525
a = 252.5
Robena is correct!
They need to sell at
least 253 tickets to
reach their goal.
We know that 189 student tickets have been sold.
a = -1/2 s + 300
a = -1/2 (189) + 300
a = -94.5 + 300
a = 205.5
If they sold 189
student tickets, then
they need 206 adult
tickets to reach their
goal of $3000.
Exit Slip
Use BOTH equations to solve.
If 45 student ticket are sold, how many
adult tickets need to be sold to reach
their goal of $3000?
X- Intercept
On the x-axis, where y = 0.
The coordinate point ( x , 0 ).
a = -1/2 s + 300
0 = -1/2 s + 300
(600, 0)
-300 = -1/2 s
s = 600
To reach their
goal, they would
have to sell 600
student tickets
and 0 adult tickets.
Y- Intercept
On the y-axis, where x = 0.
The coordinate point (0 , y ).
a = -1/2 s + 300
a = -1/2 (0) + 300 (0, 300)
a = 300
To reach their
goal, they would
have to sell 0
student tickets
and 300 adult
tickets.
1) Plot the xintercept. (600, 0)
2) Plot the yintercept. (0, 300)
3) Connect the
intercepts with a
straight-edge.
What is the rate of change between the points (600, 0) and (0, 300)?
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 Δ𝑦 𝑦2 − 𝑦1
𝑆𝑙𝑜𝑝𝑒 =
=
=
𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 Δ𝑥 𝑥2 − 𝑥1
𝐺𝑖𝑣𝑒𝑛 𝑡𝑤𝑜 𝑝𝑜𝑖𝑛𝑡𝑠 𝑥1 , 𝑦1 𝑎𝑛𝑑 𝑥2 , 𝑦2
𝟑𝟎𝟎 − 𝟎
𝟑𝟎𝟎
𝟏
𝟏
=
=
=−
𝟎 − 𝟔𝟎𝟎
−𝟔𝟎𝟎
−𝟐
𝟐
For every 2 fewer student tickets that are sold, they
must sell 1 more adult ticket.
Use the graph and equation to support your answer.
They would need to sell 100 adult tickets
to reach their goal of $3000.
No! You can’t use the graph to find the amount of
money collected, unless it’s a point on the line
because the total amount would be $3000.
S = -2a +600
They must sell 100 student tickets.
X- intercept: (300, 0). This means that to
reach their goal of $3000, they could sell
300 adult tickets and 0 student tickets.
Y-intercept: (0, 600). This means that to
reach their goal of $3000, they could sell
0 adult tickets and 600 student tickets.
The slope is 2/-1 or -2. This means that two more student
tickets sold, one less adult ticket needs to be sold.
The intercepts are opposites of each other. The x-intercept of the
1st graph is now the y intercept of the 2nd graph. The y intercept of
the 1st graph is now the x-intercept of the 2nd graph.
You can only determine when the group raises exactly $3000 . You
can not determine an exact amount of money for a point that does
not lie directly on the graph.