SOLUTION: A bag is filled with green and blue marbles. There are 117 in the bag if there are 17 more green marbles than blue marbles, find the number of Green marbles, and the number blue ma

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Question 1203506: A bag is filled with green and blue marbles. There are 117 in the bag if there are 17 more green marbles than blue marbles, find the number of Green marbles, and the number blue marbles in the bag.
The number of blue marbles is :
The number of green marbles is:
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.

Half of the sum,        i.e. %28117%2B17%29%2F2 = 134%2F2 = 67 are green marbles.


Half of the difference, i.e. %28117-17%29%2F2 = 100%2F2 = 50 are blue marbles.

Solved, in quick way.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


A quick mental solution....

Take away the "extra" 17 green marbles.
That leaves 117-17 = 100 marbles in the bag, with equal numbers of blue and green.
So there are 100/2 = 50 of each left in the bag.
Now put the 17 green ones back, giving the answer as 50 blue and 50+17 = 67 green.

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Or, if formal algebra is required....

Let x = # of blue marbles
Then x+17 = # of green marbles

The total number is 117:

x+(x+17) = 117
2x+17 = 117
2x = 100
x = 50

ANSWER: x=50 blue marbles and x+17=67 green marbles