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Real Life Systems of Linear Equations Presentation

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by

tina cao

on 24 October 2014

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Transcript of Real Life Systems of Linear Equations Presentation

Feeding Baby Hulk
Baby Hulk is responsible for a day's supply of food for herself. At the market, the price for each dog costs twice as much as the price for each cat. Baby Hulk needs to feed on/devour
164 cats and 24 dogs
. Her budget is

$4,240
. How much can Baby Hulk spend for each delicious dog or cat?
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?
Real Life Systems of Linear Equations Presentation
Step 1: Variable
Step 1: Define variable. Let x = # of student tickets were sold and y = # of adult tickets were sold
x + y = 1200
1.50x + 5y = 3200
Step 3: Solve
x + y = 1200
Eliminate y
1.50x + 5y = 3200
----------------------------
5 ---> 5x + 5y = 6000
-1---> -1.50x - 5y = -3200
----------------------------
3.5x /3.5 = 2800 /3.5
----------------------------
x = 800
Water Pitchers
By: Jasmine Sandoval, Brittany Quach, Long Nguyen, Tina Cao
800 + y = 1200
-
-800
-800
------------------
y = 400
At a high school championship basketball game
1200 tickets
were sold. Student tickets cost
$1.50 each
and adult tickets cost
$5.00 each
. The total revenue collected for the game was
$3200
. How many
student tickets were sold
? How many
adult tickets were sold?
Step 1: Set Variable
X = # of student tickets sold
Y = # of adult tickets sold
Student tickets = $1.50
Adult tickets = $5.00
Total revenue = $3200
1200 tickets were sold
Step 2: Set equation
You drove by a farmyard full of chickens and pigs. You happened to notice that there were
100 heads
and
270 legs
.

How many chicken and pigs

were there?
C: cost per cat
D: cost per dog
Needs to devour 164 cats & 24 dogs
Budget = $4,240
Farm Animals
d=2c
Step 1: Find the Variables
Step 1: Find Variables
164c+24d=$4,240
d=2c
164c+24(2c)=$4,240

Step 2: Plug it into the equation
x = chicken
y = pig
Heads = 100
Legs = 270
164c+24d=$4,240

Step 2: Equations
x + y = 100
2x + 4y = 270
Step 3: Solve

x + y = 100
2x + 4y = 270
--------------
-2 --> -2x - 2y = -200
1 --> 2x + 4y = 270
-----------------
2y/2 = 70/2
y = 35
Eliminate x
+
x + y = 100
x + 35 = 100
35 35
x = 65
-
-
Step 4: Check
2(65) + 4(35) = 270
130 + 140 = 270
Step 3: Solve

164c+24d=$4,240
164c + 24(2c) = $4,240
164c + 48c = $4,240
212c/212 = $4,240/212
c = 20

d = 2c
d = 2(20)
d = 40
Step 4: Check
164(20) + 24(40) = 4240
3280 + 960 = 4240
4240 = 4240
Step 2: Equation

Substitution
Step 3: Solve

2x + 2 + x = 8
2x + x +2 = 8
3x +2 = 8
-2 -2
-------------
3x/3 = 6/3
x = 2
y - x = 2
y - 2 = 2
+ 2 +2
y = 4
Step 4: Check

2x + y = 8
2(2) + 4 = 8
4 + 4 = 8
8 = 8

-
Check :
1.50(800) + 5(400) = 3200
1200 + 2000 = 3200
3200 = 3200 --> Correct
Step 4: Check
Basketball Games
x = small pitcher
y = large pitcher
2 small pitchers and 1 large pitcher =
8 cups
1 large pitcher minus 1 small pitcher = 2
2x + 1y = 8
y - x = 2 --> y = 2 + x
--> 2x + 2 + x = 8
note: 2 is the number of legs
that each chicken has, 4 is the number that each pig has.
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