Question

Divide a 5-inch line into two parts so that one part (a) 2 1/4 inches shorter than the other; (b) 3 times the other.

Answer 1

We have to divide 5-inch line into two parts so that one part (a) 2 1/4 inches or 2.25 inches shorter than the other; (b) 3 times the other

We can write this statement as :

(a)
`x+(x-2.25)=5`

Solving this we get

`2x=5+2.25`

`2x=7.25`

x = 3.625 inches

And the other part will be =
`5-3.625=1.375` inches

(b) As we have x+y=5

We have to find two parts where one is 3 times the other. This means we have to find x=3y

So, we have
`3y+y=5`

`4y=5`

y = 1.25 inches

Other part x is
`5-1.25=3.75` inches

Answer 2

part a), solve this system of equations:
x + y = 5
x - y = 2.25
2x = 7.25
x = 3.625
y = 1.375

part b), solve this system of equations:
x + y = 5
x = 3y
y = 1.25
x = 3.75