EXPLANATION
IQ9. You have a basket containing a certain number of red, blue, and green balls. The ratio of red to blue balls is 3:4, and the ratio of blue to green balls is 5:2. If you have a total of 63 balls, how many green balls are in the basket?
a) 12
b) 13
c) 14
d) 15
ANSWER: b) 13
EXPLANATION:
Let r, b, and g be the number of red, blue, and green balls, respectively.
We know that r/b = 3/4 and b/g = 5/2.
We can multiply these two equations to get r/g = 7/4.
We also know that r + b + g = 63.
Substituting r/g = 7/4 into the third equation, we get 7/4 * b + b + g = 63.
Simplifying the left-hand side of the equation, we get 35/4 * b + g = 63.
Multiplying both sides of the equation by 4/35, we get b + 4/35 * g = 63/35.
We know that b = 63/35 - 4/35 * g.
Substituting this into the third equation, we get 63/35 - 4/35 * g + g = 63/35.
Simplifying the right-hand side of the equation, we get g = 13/35.
Therefore, there are **13 green balls** in the basket.
