SOLUTION: Cadence has a collection of 52 dolls that all have either blue eyes or green eyes. Cadence has 16 more blue-eyed dolls than green-eyed dolls a Write a system of equations that de

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Question 214155: Cadence has a collection of 52 dolls that all have either blue eyes or green eyes.
Cadence has 16 more blue-eyed dolls than green-eyed dolls
a Write a system of equations that describes the above situation. Define your variables carefully using let statements.
b Using the system from part (a), find the number of each type of doll.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
a.
Let x=number of green eyed dolls
Ane let y=number of blue-eyed dolls
Now we are told the following:
x+y=52----------------------------------eq1
and
y=x+16------------------------------------eq2
b.
substitute y=x+16 from eq2 into eq1:
x+x+16=52 subtract 16 from each side
x+x+16-16=52-16 collect like terms
2x=36 divide each side by 2
x=18--------------------------number of green-eyed dolls
substitute x=18 into eq2
y=18+16=34----------------------number of blue-eyed dolls
CK
18+34=52
52=52
and
18+16=34
34=34
THIS PROBLEM CAN ALSO BE SOLVED USING ONE EQUATION AND ONE UNKNOWN:
Let x=number of green-eyed dolls
Then 52-x=number of blue-eyed dolls
Now we are told that:
x+16=52-x add x to and subtract 16 from each side
x+x+16-16=52-16-x+x collect like terms
2x=36-------------------same as before
Hope this helps---ptaylor