Subtracting Percents: Now company has 29% more employees than it did a year ago...

[yesssssssss]

for Problem Page



A company has recently been hiring new employees. Today the company has 29%


more employees than it did a year ago. If there are currently 51,600


employees, how many employees did the company have a year ago?

I got that 14964 is 29% of the employees they have now. I subtracted it to get 36,636 but it says that is wrong?

 

[Deleted member 4993]

for Problem Page



A company has recently been hiring new employees. Today the company has 29%


more employees than it did a year ago. If there are currently 51,600


employees, how many employees did the company have a year ago?

I got that 14964 is 29% of the employees they have now. I subtracted it to get 36,636 but it says that is wrong?

You need to calculate the #employees that the company had a year ago. So:

(#employees that the company had a year ago) + 0.29 *(#employees that the company had a year ago) = #employees that the company has now

(#employees that the company had a year ago) * (1 + 0.29) = 51600

(#employees that the company had a year ago) * (1.29) = 51600

#employees that the company had a year ago = 51600/1.29 .......................... continue

 

[stapel]

A company has recently been hiring new employees. Today the company has 29% more employees than it did a year ago.

If there are currently 51,600 employees, how many employees did the company have a year ago?

I got that 14964 is 29% of the employees they have now.

But you weren't asked about twenty-nine percent of the current workforce; you were asked about last year's workforce. So finding 29% of the current amount can't be correct.

(If you're not sure, think about it this way. You get paid, say, $20/hr. During the summer, when work is slow, they cut your pay by 50%, to $10/hr. Now, as fall approaches, they give you a raise of 50%, or $5 (being half of $10), so now you're getting paid $15/hr. Are you happy with this? Why not? Didn't they just cancel the 50% pay cut by giving you a 50% pay hike? Yes, they did; but the two fifty-percents were with respect to different starting points, so you do not end up where you'd started!)

I subtracted it to get 36,636 but it says that is wrong?

What is "it"? What did "it" "say", exactly?

You have correctly found 100% - 29% = 71% of the current workforce. But this is not the year-old workforce tally.

To learn how to set up and solve "percent of" word problems (which will explain the "hints" provided in an earlier reply), try here. Thank you!

 

[Beowulf]

Why can't you factor out the .29 before combining the terms? I see that it doesn't work, but don't really get why.

.29x+x=51600
.29x/.29+x=51600/.29
2x=177,931.0345
x=... ok so this is clearly wrong, but I don't really understand on a gut level why.

I guess it is the difference between factoring a single number and factoring both.

So I would need to factor .29 out of the 2nd term also?
no. .29x/.29+x/.29=51600/.29 doesn't work.

I think I almost understand why but not exactly.

 

[mmm4444bot]

Why can't you factor out the .29 before combining the terms?

In order to factor 0.29 from an expression, each term in the expression must contain at least one factor of 0.29 -- in your algebraic equation, only one term on the left-hand side contains a factor of 0.29; therefore, you may not factor out 0.29.

.29x + x = 51600

.29x/.29 + x = 51600/.29

The second line above does not show factoring; it shows division.

When you divide an expression containing more than one term, each term in that expression must be divided.

Two terms comprise the left-hand side of your equation (0.29x and x), so each must be divided.

0.29x/0.29 + x/0.29 = 51600/0.29

x + x/0.29 = 51600/0.29


Here's another approach, which you might like: combine like-terms, as the first step.

0.29x + x = 51600

1.29x = 51600

Continue. :cool: