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?

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

Half of the green bricks removed.

so, the number of green bricks would be

One-third of blue bricks are added.

So, the number of blue bricks would be

so, Total number of bricks now becomes

According to question, it becomes,

so, original number would be

New number would be

so, twice the original =

Difference between them  is given by

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

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

br

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 =   (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4   we need to find some relationship between a and b.

let's try ab = bc  

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2 

br = sqrt(3) * a

cp

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram. 

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a 

cp = sqrt(3)*a

aq

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a 

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt  3) * a which agrees with the other two.

60: 45 =12: 9 =4: 3 so the answer is 4: 3