Algebra???

Question

Colored copies cost 10 cents per copy and white copies cost 5 cents per copy. Sandy made 400 copies, some of which were colored and the rest white. Her total bill was $22.50. How many colored copies and how many white copies did she make.

Please tell me how you solved it and the equation.

Answer 1

you have to use simultaneous equations.

let x be the number of coloured copies and y be the number of white copies.

10x + 5y = 2250 ...(1)
x + y = 400 ...(2)

(2) x 5:
5x + 5y = 2000 ...(3)

(1) - (3):
5x = 250
x = 50

subst. x = 50 into (2)
50 + y = 400
y = 350

She made 50 coloured and 350 white copies.

Answer 2

Analysis.

1. Total number of copies = 400

Let w = white copies, c = colored, then, w + c = 400

2. Total cost = $ 22.50

0.05w + 0.10c = 22.50

Now, you have 2 equations in 2 unknows. You can solve in any methods you're comfortable with: SUBSTITION, ELIMINATION, MATRICES, etc. including ESTIMATION.

In this case, Substitution is easiest to do.

c = 400 - w , thus the 2nd eqn becomes

0.05w + 0.10(400-w) = 22.50
(note: the choice of variable is because it is easier to multiply by .10, just a little trick for efficiency) Distribute 0.10 and simplify

0.05 w + 40 -0.10w = 22.50
-0.05 w = 22.50 -40
-0.05 w = -17.50, both negative signs cancel
w = 350 copies of white
therefore 50 colored copies.

Check: white: 350x0.05per = $17.50
colored 50x.10per = $ 5.00
TOTAL $ 22.50

Answer 3

10y+5k =2250 cents ......(1)....and y +k=400......so k=400 -y

do that in (1)
so 10y +5(400-y)=2250 , 10y+2000-5y=2250,
5y=2250-2000 , 5y=250 ,y=250/5 ,y=50
so 50 colored and 350 white.

Answer 4

.05(x) + .10(400-x) = 22.50
.05x + 40 - .10x = 22.50
-.05x + 40 = 22.50
-.05x = -17.50
-17.50/-.05 = x
x = 350
There are 350 5cent (black and white) copies, and 400-350 (50) color copies.

Answer 5

w- 350
c - 50