SOLUTION: A woman is paid $20 for each day she works and forfeits $5 for each day she is idle. At the end of 25 days she nets $450. How many days did she work?

Question 936086: A woman is paid $20 for each day she works and forfeits $5 for each day she is idle. At the end of 25 days she nets $450. How many days did she work?
Found 2 solutions by pricerk, Theo:
Answer by pricerk(1) (Show Source): You can put this solution on YOUR website!
x+y=25 where x is the number of days worked and y is days missed
20x-5y=450 $20 per day worked , -5 per day lost when not working
y=25-5
using substitution
20x -5(25-x) =450
20x - 125 -5x =450
15x-125=450
15x=450+125=575
x=575/15 = 23
x=23
x+y=25 23+y=25 y=25-23=2
20x-5y=460-10=450
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x equal the number of days she is working.
let y equal the number of days she is idle.
total number of days is 25.

x + y = 25

when she works, she makes 20 dollars.
when she is idle she loses 5 dollars.
she makes a total of 450 dollars.

20x - 5y = 450

you have 2 equations that need to be solved simultaneously.

they are:

x + y = 25
20x - 5y = 450

solve for y in the first equation of x + y = 25 to get:

y = 25 - x

replace y with 25 - x in the second equation of 20x - 5y = 450 to get:

20x - 5 * (25 - x) = 450

simplify to get:

20x - 125 + 5x = 450

combine like terms to get:

25x - 125 = 450

add 125 to both sides of the equation to get:

25x = 575

divide both sides of the equation by 25 to get:

x = 23

she worked 23 days and she was idle 2.

she made 23 * 20 = 460 and she lost 2 * 5 = 10 to net a total of 450 dollars.

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