Transcript Solving Equations_8.EE.3.7x

BELLWORK
The PTSO of West-East HS were selling tickets
for the game against their rival, North-South HS.
The PTSO received a $1500 donation from a
booster and adult tickets cost $5. How many
adults attended the game if the PTSO’s total
sales were $3900.
Write an equation that represents this problem,
then solve.
SOLVING EQUATIONS
Lundy and his sister wanted to save money for
an upcoming vacation. They both had $20 in
their bank account and they receive $10 per
week for allowance. Their cousin is going on the
same trip. She had $60 in her account and she
receives $15 per week for allowance. Lundy and
his sister are competing with their cousin to see
who can save more money. How many weeks
will it take for Lundy and his sister to save up
the same amount of money as their cousin?
QUESTION #1
Lundy and his sister wanted to save money for
an upcoming vacation. They both had $20 in
their bank account and they receive $10 per
week for allowance. Their cousin is going on the
same trip. She had $40 in her account and she
receives $20 per week for allowance. Lundy and
his sister are competing with their cousin to see
who can save more money. How many weeks
will it take for Lundy and his sister to save up
the same amount of money as their cousin?
QUESTION #2
Lundy and his sister wanted to save money for
an upcoming vacation. They both had $20 in
their bank account and they receive $10 per
week for allowance. Their cousin is going on the
same trip. She had $45 in her account and she
receives $20 per week for allowance. Lundy and
his sister are competing with their cousin to see
who can save more money. How many weeks
will it take for Lundy and his sister to save up
the same amount of money as their cousin?
SOLVING EQUATIONS
6x  4  2x  3
5x  3  5x  5
6 x  4  2(3 x  2)
SOLVING EQUATIONS
EXTENSION
The PTSO of West-East HS were selling tickets
for the game against their rival, North-South HS.
They sold 400 more student tickets than adult
tickets and half as many child (under high
school age) tickets as adult tickets. Adult tickets
cost $5, student tickets cost $3 and the
children tickets cost $2 each. Total sales for the
PTSO were $3900.
How many adults attended the game?
WHAT SHOULD WE KEEP IN MIND?
• 400 more student tickets were sold than
adult tickets.
• Half as many child tickets (under high
school age) were sold compared to adult
tickets.
• Adult tickets cost $5 each, student
tickets cost $3 each and child tickets
cost $2 each.
• Total sales for the PTSO were $3,900.
WHAT QUESTIONS MUST WE ANSWER?
For what are we trying to solve?
 How can we represent this with an equation?

Let a represent the number of adult tickets sold
 Identify other entities

 Student
tickets
 Child tickets
QUESTIONS TO ANSWER

Identify other entities


Student tickets
How can we represent the number of student
tickets?
400 more student tickets were sold than adult
tickets
 a + 400 can represent the number of student
tickets sold

QUESTIONS TO ANSWER

Identify other entities

Child tickets
How can we represent the number of child
tickets sold?
 They sold half as many child tickets as adult
tickets

a

2 represents the number of child tickets sold
PUT IT ALL TOGETHER
ADULT tickets: Let a represent the number
of adult tickets sold
STUDENT tickets: a + 400 represents the
number of student tickets sold
CHILDREN tickets:
a
represents the
2
number of children tickets sold
Total Sales : $3900
PUT IT ALL TOGETHER
Adult tickets cost $5, student tickets cost $3
and the children tickets cost $2.
 The PTSO made $3900.
 How can we represent this with an equation?

$5 (a) + $3 (a+400) +
# of
adult
tickets
# of
student
tickets
a
$2( 2 )
# of
child
tickets
= $3900
Total
MAKE SENSE…
• How many adult tickets were sold?
• How many student tickets were sold?
• How many children tickers were sold?
SOLVE TO FIND THE NUMBER OF ADULT TICKETS SOLD
a
2( 2 )
5 (a) + 3 (a+400) +
= 3900
5a + 3a + 1200 + a = 3900
9a + 1200 = 3900
9a + 1200 - 1200 = 3900 - 1200
9 = 2700
9
9
a = 300
HOW MANY STUDENTS? CHILDREN?

a = 300 adults attended the game

How many students?


a + 400 = student tickets, 300 +400 = 700 students attended
How many children?
a = child tickets, 300/2=150 children attended

2
SOLUTIONS
One solution
 Infinitely Many Solutions



Two equations with the same rate of change and
ultimately the same constant (after simplifying
using distributive property)
No Solution

Two equations with same rate of change but
different constants
QUIZ

A.
B.
C.
D.
Pear Cellphone Company charges a monthly charge of
$12.95 and $0.25 a minute per call. The bill for one
month is $31.20. How many minutes were used?
Write an equation for this problem and solve to find the
amount minutes used for the month.
What if you compared this company with the
competitor, Banana Cellphone Company, who charges
the $0.15 a minute rate but their monthly charge is
$25.95. At what point (number of minutes) would the
bills for each company be the same?
How many solutions are there?
Which company would you choose? Why?