1990 AMC 8 Problem 14

Attempt Problem 14 of the 1990 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1990 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

14.

A bag contains only blue balls and green balls. There are 66 blue balls. If the probability of drawing a blue ball at random from this bag is 14,\dfrac14, then the number of green balls in the bag is
1212
1818
2424
3030
3636
Answer: B
Concepts:basic probabilityratio and proportion
Small hint:
If the probability of blue is 14,\dfrac14, then blue balls are a quarter of the total
Big hint:
Use 66 blue balls to find the total, then subtract to get the green balls
Solution:
Since blue balls make up 14\dfrac14 of the bag and there are 66 of them, the total is 6⋅4=246 \cdot 4 = 24 balls.
So the number of green balls is 24−6=1824 - 6 = 18.
Thus, the correct answer is B .
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