Question

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

Answer 1

110 red bricks she add in order to double the total number of bricks

Explanation:

Kali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1.

The original ratio of red, green and blue is 4x, 3x and x

the total of the original is
`4x+3x+x=8x`

She then removes 1/2 of the green bricks

she remove
`(3)/(2)x`

adds 1/3 more blue bricks

`x+(1)/(3)x=(4)/(3)x`

The total of new is
`4x+(3)/(2)x+(4)/(3)x=(41)/(6)x`

size is reduced by 14 bricks

total of original - total of new = 14

`8x -(41)/(6)x=14`

`(7)/(6)x=14`

multiply both sides by 6/7

x= 12

original number of bricks = 8x = 8 times 12= 96

total of new bricks =
`(41)/(6)(12)=82`

Double the original number =
`2 \cdot 96 = 192`

the number of red bricks needs to add is

`192-82=110`

110 red bricks she add in order to double the total number of bricks