A2D2 wrote:
Bunuel wrote:
Bunuel wrote:
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
Original ratio = R:G:B = 4x:3x:x.
Original total = 4x + 3x + x = 8x.
The new number of bricks: 4x, 3x/2, 4x/3.
New total = 4x + 3x/2 + 4x/3 = 41x/6.
We are told that {Original total} - {New total} = 14 --> 8x - 41x/6 = 14 --> x = 12.
Original total = 8x = 96;
New total = 41x/6 = 82.
To double the original number of bricks, or simply to have 2*96 = 192 bricks, she need to add 192 - 82 = 110.
Answer: C.
How to know where to take different variables and where same, I tried taking x,y,z and got stuck
Notice that if we reduce x we get the given ratio of 4:3:1. If you use x, y, and z instead, you don't get the original ratio.
x there is a positive multiple (1, 2, 3, ...), which shows that the number of red, green, and blue bricks could be:
4*1 = 4, 3*1 = 3, and 1*1 = 1, for x = 1;
4*2 = 8, 3*2 = 6, and 1*2 = 2, for x = 2;
4*3 = 12, 3*3 = 9, and 1*3 = 3, for x = 3;
...
Generally, if we are told that say the number of boys to girls in a certain class is 2 to 1, then this could be expressed as B:G = 2x:x, where x is a positive multiple.
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