Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes $\frac{1}{2}$ of the green bricks and adds $\frac{1}{3}$ 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?

Correct answer marked below

110

Correct

120

192

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Explanation

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Official Explanation

Official

Original ratio: R:G:B = 4x:3x:x.

Original total = 4x + 3x + x = 8x.

New number of bricks:

- Red remains 4x.

- Green becomes

\frac{3x}{2}

.

- Blue becomes

x + \frac{x}{3} = \frac{4x}{3}

.

New total =

4x + \frac{3x}{2} + \frac{4x}{3} = \frac{41x}{6}

.

We are told that Original total - New total = 14:…

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What this question tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.