Percentage change

[Deryl]

Hello!
I need your help with one of my exercise.
I have made calculation but I don't know if this is a good answer.
This is the content of this exercise:
1) At the beginning of the year women were 50% of all hired employees in some company.
Because of the financial issues at the end of the year the company decided to reduce 30% of job places. After this reduction women were only 40% of all employees.
By how many percentage the quantity of women at the end of the year has changed compared to the quantity of women at the beginning of the year?

I have made those calculations:
x - all of employees at the beginning of the year
x * 50% = 1/2 x − quantity of women at the beginning of the year

x − 30% x = x − 3/10 x = 7/10 x − all of employees at the end of the year
7/10 * 40% x = 7/10 x * 4/10 x = 7/25 x − quantity of women at the end of the year

1/2x − p% * 1/2x = 7/25
− p% * 1/2 x = 7/25 x − 1/2 x
− p% * 1/2 x = − 44/200 x
p = 88/200 x = 44/100 x
p= 44/100 x * 100% = 44%

Answer: Quantity of women at the end of the year were decreased of 44% compared to their quantity at the beginning of the year.

Please let me know if this is a correct answer. I'll be very grateful

 

[Dr.Peterson]

That looks good. I'll do it a slightly different way as a check:

# employees at start: x
# women at start: 0.50x
# employees at end: 0.70x
# women at end: 0.40*0.70x = 0.28x
# women at end/#women at start: (0.28x)/(0.50x) = 0.56

So 56% of the women remain, which is a decrease of 44%.

You are right.

 

[Deryl]

That looks good. I'll do it a slightly different way as a check:

# employees at start: x
# women at start: 0.50x
# employees at end: 0.70x
# women at end: 0.40*0.70x = 0.28x
# women at end/#women at start: (0.28x)/(0.50x) = 0.56

So 56% of the women remain, which is a decrease of 44%.

You are right.

Thank you for your answer!

Your way with decimal numbers looks much transparent than mine with using fractions.