March 28, 2014
Warm Up
1. Solve the system:
x + 2y = 7
3x – 2y = 5
3/28/14
3/28/14
2. Determine if the system of equations
has no solution or many solutions,
and why. Show your work.
y = -5x + 2
5x + y = -1
3. You went to the movies and got 2 large popcorns and 4 sodas and it
cost $28.00. Your friends went the other day and got 3 large popcorns and
5 sodas and it cost them $38.00.
- Score a 70%
or better on the
unit 3 assessment
Write a system of equations to model the above situation.
Today we are going to review the 3
different ways to solve a system.
You are going to be given a word
problem and solve it the 3 different
ways.
Let's just practice how to write the equations.
The school that Stefan goes to is selling tickets to a choral performance.
On the first day of ticket sales the school sold 3 senior citizen tickets and 1
child ticket for a total of $38. The school took in $52 on the second day by
selling 3 senior citizen tickets and 2 child tickets. Find the price of a senior
citizen ticket and the price of a child ticket.
March 28, 2014
Write the
problem and
then
Solve the
system
write the two
equations in
this box.
by graphing
in this box.
Solve the
system
Solve the
system
using
substitution in
this box.
using
elimination in
this box.
Problem 1:
I will put you in groups of 3.
This means that you can
each pick a method and work
on your section of the poster.
However you must ALL check
each others work to be sure
it's done correctly.
Problem 2:
The admission fee at a small fair is $1.50 for children and
$4.00 for adults. On a certain day, 2200 people enter the
fair and $5050 is collected. How many children and how
many adults attended?
• number of adults: a
• number of children: c
• total number: a + c = 2200
• total income: 4a + 1.5c = 5050
Two small pitchers and one large pitcher can
hold 8 cups of water. One large pitcher minus
one small pitcher constitutes 2 cups of water. How many cups of water can each pitcher hold?
Let x = small pitcher
y = large pitcher
2x + y = 8
y-x=2
March 28, 2014
Problem 4:
Problem 3:
A few families took a trip to an amusement park together. Tickets cost
$6.00 each for adults and $2.50 each for kids, and the group paid
$38.00 in total. There were 5 fewer adults than kids in the group.
Let x equal the number of adults and y equal the number of kids.
The system of equations is then:
6x+2.5y=38
x=y−5
Problem 5:
All of the 5th grade teachers and students from Loyola went
on a field trip to an art museum. Tickets were
$6.50 each for teachers and $4.00 each for students, and the
group paid $53.00 in total.
The next month, the same group visited a natural history
museum where the tickets cost $26.00 each for teachers and
$7.50 each for students, and the group paid $127.00 in total.
Let x equal the number of teachers and y equal
the number of students.
The system of equations is:
6.5x+4y=53
26x+7.5y=127
The drama club sold bags of candy and cookies to
raise money for the spring show. Bags of candy cost
$6.00, and bags of cookies cost $2.50, and sales
equaled $41.50 in total. There were 3 more bags of
cookies than candy sold.
Let x equal the number of bags of candy and y equal the
number of bags of cookies.
The system of equations is then:
6x+2.5y=41.5
y=x+3
Problem 6:
A woman owns 21 pets. Each of her pets is either a cat or a bird.
If the pets have a total of 76 legs, and assuming that none of the
bird's legs are protruding from any of the cats' jaws, how many
cats and how many birds does the woman own?
x be the number of cats the lady owns, and
y be the number of birds the lady owns.
x + y = 21
4x + 2y = 76
March 28, 2014
Problem 7:
You've gone to a fruit stand to get some fresh
produce. You notice that the person in front of you
gets 5 apples and 4 oranges for 10 dollars. You get 5
apples and 5 oranges for 11 dollars.
Let x = Price of apples
Let y = price of oranges
5x + 4y = 10
5x + 5y = 11
Let's present our problems