Question

Suppose i have a pieces of woods,and i have to cut in two pieces ,one is shorter,the other is longer,is its 20 feet long,I want to cut in two pieces.in such way than,5 times the length of the shorter is 2 feet more than the length of the longer the question is to find how many feet is long of them?or how many each feet?

Answer 1

if the original segment, was 20ft long
then you cut it in two
say
a b
-------------------------------------------
^
cut it here

so, the shorter side is "a"
and the longer is "b"

notice, originally it was a 20ft long
so, whatever the pieces are, must
add up to 20
thus
a + b = 20

now
5 times the smaller
5*a or 5a

equals 2 more than the longer
b + 2

so 5a = b +2


`\bf \begin{cases} a+b=20\implies b=\boxed{20-a}\\ 5a=b+2\\ ---------\\ 5a=\boxed{20-a}+2 \end{cases}`

solve for "a", to get the shorter one

what's the longer one? well, 20 - a