Question

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

Answer 1

Answer: There are 110 red bricks that she will need to add in order to double the total number of bricks.

Step-by-step explanation:

Since we have given that

Ratio of red, green and blue toy bricks in the ratio of 4:3:1.

Let the number of red toy bricks be 4x.

Let the number of green toy bricks be 3x.

Let the number of blue toy bricks be x.

Total number of bricks would be $4x+3x+x=8x$

Half of the green bricks removed.

so, the number of green bricks would be $\dfrac{3x}{2}$

One-third of blue bricks are added.

So, the number of blue bricks would be $x+\dfrac{x}{3}=\dfrac{3x+x}{3}=\dfrac{4x}{3}$

so, Total number of bricks now becomes

$4x+\dfrac{3x}{2}+\dfrac{4x}{3}\\\\=\dfrac{41x}{6}$

According to question, it becomes,

$8x-\dfrac{41x}{6}=14\\\\\dfrac{48x-41x}{6}=14\\\\\dfrac{7x}{6}=14\\\\x=\dfrac{14\times 6}{7}\\\\x=12$

so, original number would be $8x=8\times 12=96$

New number would be $\dfrac{41}{6}\times 12=82$

so, twice the original = $2\times 96=192$

Difference between them  is given by

$192-82=110$

Hence, there are 110 red bricks that she will need to add in order to double the total number of bricks.