9514 1404 393
Answer:
4
Step-by-step explanation:
The 10 non-yellow counters in the bag represent 5/7 of the total number of counters, c.
10 = (5/7)c
10(7/5) = c = 14
There are 14 counters in the bag, of which 14-10 = 4 are yellow.
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<em>Alternate solution</em>
Let y represent the number of yellow counters in the bag. The probability of drawing a yellow counter is the number of yellow counters divided by the total number of counters:
y/(y +3 +7) = 2/7
Multiply both sides of this equation by 7(y+10) to get ...
7y = 2(y +10)
7y = 2y +20 . . . . eliminate parentheses
5y = 20 . . . . . . . . subtract 2y
y = 20/5 = 4 . . . . divide by the coefficient of y
There are 4 yellow counters in the bag before any are taken.
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<em>Another alternate solution</em>
If the probability of yellow is 2/7, the ratio of yellow (y) to non-yellow is ...
yellow : non-yellow = 2 : (7-2) = 2 : 5 = y : (3+7) = y : 10 = 4 : 10
⇒ y = 4
There are 4 yellow counters in the bag.
