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Writing Systems of Equations from Word Problems
Contributed by: Ramos
(Original author: Koval)
Select the system of
equations that could
represent the problem
situation and solve.
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?
b + g = 24    g = 2b
b + 2g = 24    b + g = 2
            boys and              girls are in theScience Squad at Hightown Middle School.
b + g = 24    b = 2g
b + 2g = 24    b = g
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?
Fredward should buy              bottles of juiceand              bottles of soda for his birthday party.
j + s = 29    j + s = 12
j = 3
    s = 2
3j + 2s = 29      j + s = 12
3j = 29
    2s = 12
440 adults and students attended the Drumond High 
School orchestra concert.  Forty more adults than
students attended.  How many of each went to the
concert.
               adults and              students attended theDrumond High School orchestra concert.
a + 40 = 440
    s = 440
a + s = 440    a = s + 40
a + s = 440
    s = a + 40
a + s = 440
    a = 40s
At Cinemania Movie Theater, movie tickets for a family 
of 2 adults and 3 children cost $28.  Tickets for a family
of 1 adult and 2 children cost $22.  How much does an
adult ticket and a child ticket cost?
Cinemania Movie Theater charges $          for an
adult ticket and $         for a child ticket.
a = 2 + 1    c = 3 + 2
2 + a + 3 + c = 28
    1 + a + 2 + c = 22
2a + 3c = 22
     a + 2c = 28
2a + 3c = 28    a + 2c = 22
Cal is planting a garden.  He wants to fill it with tulips
and daisies.  Each tulip bulb cost $2.00, each daisy
bulb cost $1.50.  He has $45 to spend on these flowers.
He wants five less than twice as many tulips as daisies.
How many of each flower should he buy?
Cal should buy            tulip bulbs and           daisybulbs to plant in his garden.
2t + 1.50d = 45
    t = 2d - 5
2t + 1.50 = 45
    d = 2t - 5
t = 2.00
    d = 1.50
2t + 1.50d = 45
    t = 2d + 5
The sum of two numbers is 52.  Their difference is 10.
xy = 52
    x/y = 10
x + y = 10    x - y = 52
x =             and y =             
x = 52
    y = 10
x + y = 52    x - y = 10
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