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2.21 Systems in Words
Contributed by: Smith
(Original author: Koval)
Select the correctsystem of equationsfor the followingproblem.
There are twice as many girls as boys in the Science Squad at Hightown Middle School. If 24 students are in the club, then how many are boys,and how many are girls?
2nd equation: number of girls compared to boys
1st equation: total students in the club
b + g = 24    g = 2b
b + 2g = 24    b + g = 2
b + g = 24    b = 2g
b + 2g = 24    b = g
There are twice as many girls as boys in the Science 
Squad at Hightown Middle School.  If 24 students are 
in the club, how many of them are boys and how many 
are girls?
boys (b)
10
6
7
8
9
girls (2b)
12
There are twice as many girls as boys in the Science 
Squad at Hightown Middle School.  If 24 students are 
in the club, how many of them are boys and how many 
are girls?
boys (b)
10
6
7
8
9
girls (2b)
12
14
16
18
20
6-12
7-14
8-16
9-18
10-20
All rows have twice asmany girls as boys.
Click next to the row that ALSO has24 total students
You can solve by
SUBSTITUTION...
Twice as many girls as boys. Total: 24 students.
b + g = 24
     
g = 2b
The MEAT of the problem was:
Substitute
Original
Combine b's
Solve
b +            = 24
b + g = 24
     
b =
  = 24
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
Money Spent Equation
?
Total Bottles Equation
?
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
j + s = 29    j + s = 12
j = 3
    s = 2
3j + 2s = 29      j + s = 12
3j = 29
    2s = 12
    3j + 2s = 29      j +   s = 12
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
Yes, a pair cancels out to zero when combined
No, no pair cancels out to zero when combined
Cannot be Determined - Too many numbers
Are ANY of these pairs
of like terms
ZERO PAIRS?
    3j + 2s = 29      j +   s = 12
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
Add
Since there are no zero pairs, what operationcan we do to either equation to CREATE one?
Subtract
Multiply
square root
    3j + 2s = 29      j +   s = 12
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
Fill in the BLANK to
create a ZERO pair
+ 2s
s
    3j + 2s = 29      j +   s = 12
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
What number should youmultiply the second equation byto change +s to -2s?
* ?
+2s
-2s
    3j + 2s = 29      j +   s = 12
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
Fill in the missing coefficients and constantto rewrite the old equation,    j + s = 12,to the new equation.
*
(-2)
  3j  +2s  = 29
j       s =
    3j + 2s = 29      j +   s = 12
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
*
(-2)
 j+ s = 5
 j - s = -5
Combining the equations
yields which sum ???
  3j +2s  =  29
-2j -2s  = -24
 j = 5
 j = -5
    3j + 2s = 29      j +   s = 12
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
Ok, so j = 5,which equationcan you substitute 5 for jto solve in ONLY 1 STEP?
*
(-2)
3j + 2s = 29     
  j +   s = 12
  3j +2s  =  29
-2j -2s  = -24
j   = 5
    3j + 2s = 29      j +   s = 12
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
Solve
for S
*
(-2)
  3j +2s  =  29
-2j -2s  = -24
j   = 5
  j +   s = 12
    +   s = 12
5
s =
    3j + 2s = 29      j +   s = 12
Fredward is buying juice and soda for his birthday
party.  He wants to buy 12 total bottles and can spend
$29.  If juice cost $3 per bottle and soda cost $2
per bottle, how many bottles of each should he buy?
The SOLUTION5 juices and 7 sodaswill make which of the original equations true ???
  j +   s = 12
3j + 2s = 29
BOTH
NEITHER
*
(-2)
  3j +2s  =  29
-2j -2s  = -24
j   = 5
FINITO
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