Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes (1/2) of the green bricks and adds (1/3) more blue bricks, reducing the size of the tower by 14 bricks. How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?
A) 82
B) 96
C) 110
D) 120
E) 192
Since the number of green bricks decreases by 1/2, the number of green bricks must be EVEN.
Since the number of blue bricks increases by 1/3, the number of blue bricks must be a MULTIPLE OF 3.
Thus, the MULTIPLIER for the ratio must be an EVEN MULTIPLE OF 3 -- in other words, a MULTIPLE OF 6.
Multiplying R:G:B = 4:3:1 by 6, we get:
R=24, G=18, B=6.
Here, if 1/2 of the green bricks are removed, and the number of blue bricks increases by 1/3, the net change = -(1/2 * 18) + (1/3 * 6) = -9 + 2 = -7.
To double the net change to -14, all of the values in the ratio must also DOUBLE:
R=48, G=36, B=12.
Thus:
T = 48+36+12 = 96 bricks.
After 14 bricks are removed, the remaining number of bricks = 96-14 = 82.
To increase this value to double the original number of bricks -- 192 -- the number of additional bricks needed = 192-82 = 110.
The correct answer is
C.
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