SOLUTION: Grandma prepared 80 sandwiches for her 30 grandchildren.
Each grandchild took either 2 or 3 sandwiches.
There were no sandwiches left.
How many grandchildren took 3 sandwiches
Question 1157997: Grandma prepared 80 sandwiches for her 30 grandchildren.
Each grandchild took either 2 or 3 sandwiches.
There were no sandwiches left.
How many grandchildren took 3 sandwiches each?
x = # who took 2 sandwiches each
y = # who took 3 sandwiches each
x+y=30 [there are 30 grandchildren]
2x+3y=80 [there are 80 sandwiches]
Solve by your favorite method.
Note if you prefer you can set it up using a single variable:
x = # who took 2 sandwiches each
30-x - # who took 3 sandwiches each
2(x)+3(30-x) = 80
Informally, using logical reasoning (if a formal algebraic solution is not required)....
Have each of the 30 grandchildren take 2 sandwiches. That is 60 of the total 80 sandwiches; there are 20 left. Each of 20 grandchildren takes a third sandwich.
ANSWER: 20 grandchildren took 3 sandwiches each.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website! Largest number divisible by 3 is 78
2 sandwiches left, but 4 children left
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5 sandwiches left -not divisible by 2
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8 sandwiches left, but 6 children left
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11 sandwiches left -not divisible by 2
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14 sandwiches left, but 8 children left
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17 sandwiches left
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20 sandwiches left for the 10 remaining children
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20 grandchildren took 3 sandwiches each
and the 10 remaining took 2 sandwiches each
Answer by MathTherapy(10557) (Show Source): You can put this solution on YOUR website! Grandma prepared 80 sandwiches for her 30 grandchildren.
Each grandchild took either 2 or 3 sandwiches.
There were no sandwiches left.
How many grandchildren took 3 sandwiches each?
Let number that took 3 sandwiches be L
Then numebr that took 2 sandwiches = 30 - L
We then get: 3L + 2(30 - L) = 80
3L + 60 - 2L = 80
3L - 2L = 80 - 60
Number that took 3 sandwiches, or
That's ALL!!