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.
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
Answer:
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