SOLUTION: 840 stickers were given to 42 children. 2/3 of the children were boys, and each of them received the same number of stickers. Each girl received twice a many stickers as each boy.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 840 stickers were given to 42 children. 2/3 of the children were boys, and each of them received the same number of stickers. Each girl received twice a many stickers as each boy.       Log On


   

Question 657439: 840 stickers were given to 42 children. 2/3 of the children were boys, and each of them received the same number of stickers. Each girl received twice a many stickers as each boy. How many stickers did each girl receive?
I do not have any idea where to even begin with this word problem....
the only concept I have in my head is
42=%282%2F3%29x%2B2%28%282%2F3%29x%29
and that just looks completely wrong.

Found 4 solutions by htmentor, ewatrrr, solver91311, MathLover1:
Answer by htmentor(1343) About Me  (Show Source):
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If there are 42 children, and 2/3 are boys, that means there are (2/3)42 = 28 boys and 14 girls
Let s = the number of stickers received by the boys
Then each girl received 2s stickers
We can write the following equation for the total number of stickers:
840 = 28s + 14(2s) = 56s
s = 840/56 = 15
So the boys got 15 stickers and the girls got 30 stickers

Answer by ewatrrr(24785) About Me  (Show Source):
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Hi,

42 children, 2/3 of the children were boys ⇒  28 boys and  14 girls

Each boy received the same number of stickershighlight%28x%29, girls highlight%282x%29

Question states***840 stickers

  28x + 14·2x = 840

     56x = 840

       x = 15, number of tickets each boy had.  Each girl had 30 tickets.

and...

 28%2A15+%2B+14%2A30+=+840

Answer by solver91311(24713) About Me  (Show Source):
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Sometimes appearances can be deceiving. However, that is NOT the case here. Your equation looks completely wrong for the most obvious of reasons; it is completely wrong. That fact leads us to the very best starting place: The beginning.

If there are 42 children and of them are boys, then there are boys; from which it should be obvious (since is half of ) that there are 14 girls.

Let represent the number of stickers each boy received, and then must be the number of stickers each girl received. Since there are 28 boys each of whom received stickers, the total number of stickers received by boys is . Similarly, the total number of stickers received by girls is . Then, since the sum of and is 1, we can be certain that there were no transgender people in the group of children (hey, you never know these days) so we can make the assertion that the number of stickers given to boys plus the number of stickers given to girls is equal to the total number of stickers given. So:



Solve for and then calculate

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by MathLover1(20850) About Me  (Show Source):
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given:
840 stickers
42 children; boys b and girls g
+2%2F3 of the 42 children were boys, and each of them received the same number of stickers x
Each girl received twice a many stickers as each boy, which is 2x
_________________________________
if 42 children; boys b and girls g, then
b%2Bg=42........1
+2%2F3 of the 42 children were boys, then
+b=%282%2F3%2942 ...->...+b=84%2F3 .->...+highlight%28b=28%29
then g=42-b ..->...+g=42-28 .->...highlight%28+g=14%29

then 840 stickers is a sum of b%2Ax%2Bg%2A2x=840...plug in values for boys b and girls g
x%2B2x=840
3x=840
x=840%2F3
x=280...........the number of stickers that boys got
then
x=280%2F28=highlight%2810%29...........the number of stickers that each boy got
since girls got 2x then they got %282%2A280%29%2F14=highlight%2840%29 stickers

check the sum of stickers
28b%2B14g=840
28%2A10%2B14%2A40=840
280%2B560=840
840=840