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

Answer:

$a = 18x$

Step-by-step explanation:

Given

$\frac{1}{2}(a + d) = 10x$

$\frac{1}{2}(b + c) = 8x$

$\frac{1}{3}(b + c+d) = 6x$

Required

The value of (a)

We have:

$\frac{1}{2}(a + d) = 10x$ --- multiply by 2

$\frac{1}{2}(b + c) = 8x$ --- multiply by 2

$\frac{1}{3}(b + c+d) = 6x$ --- multiply by 3

So, we have:

$\frac{1}{2}(a + d) = 10x$

$a + d = 20x$

$\frac{1}{2}(b + c) = 8x$

$b + c = 16x$

$\frac{1}{3}(b + c+d) = 6x$

$b + c + d= 18x$

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)

$a = 20x - 2x$

$a = 18x$