Question

divide 80 into two numbers such that 5 times one number =3 times the other number

Answer 1

Let the 2 numbers be x and y.
According to the question   x+y = 80
It is given that 5x = 3y
                       x=3y÷5
x+y=3y÷5+y=80
8y÷5=80
8y=80×5=400
y=400÷8=50
x+y=80
x+50=80
x=80-50=30
The 2 numbers are 30 and 50.

Answer 2

From the given data,
x+y=80 (eqn 1)
and 5x=3y (eqn 2)
Therefore, x=3y/5 (from eqn 2)

substituting value for x from above to eqn 1

3y/5 + y = 80
3y + 5y = 80 × 5
8y = 80 × 5
y = 50

Therefore,
x=80-y
x=30

The numbers are 30 and 50.