Question

the average length of string a and string d is 10x cm. the average length of string b and string c is 8x cm . the average length of strings b , c , d is 6x cm . find the length of string a in terms of x

Answer 1

`a = 18x`

Explanation:

Given

`(1)/(2)(a + d) = 10x`

`(1)/(2)(b + c) = 8x`

`(1)/(3)(b + c+d) = 6x`

Required

The value of (a)

We have:

`(1)/(2)(a + d) = 10x` --- multiply by 2

`(1)/(2)(b + c) = 8x` --- multiply by 2

`(1)/(3)(b + c+d) = 6x` --- multiply by 3

So, we have:

`(1)/(2)(a + d) = 10x`

`a + d = 20x`

`(1)/(2)(b + c) = 8x`

`b + c = 16x`

`(1)/(3)(b + c+d) = 6x`

`b + c + d= 18x`

Substitute
`b + c = 16x` in
`b + c + d= 18x`

`16x + d = 18x`

Solve for d

`d = 18x - 16x`

`d = 2x`

Substitute
`d = 2x` in
`a + d = 20x`

`a + 2x = 20x`

Solve for (a)

`a = 20x - 2x`

`a = 18x`