please can someone tell me where i am wrong.
Directions:
Translate to a system of equations and solve.
Problem:
Colored copies cost 10cents per copy and white copies cost 5cents per copy. Sandy made 400 copies, some of which were colored and the rest white. Her total bill wa $22.50. How many colored copies and how many white copies did she make?
My answer and solving this is what i get and the steps I used.
x for white coies and y for color
First equation:
x + y = 400
Second equation:
10x + 5y = 22.50
From the first equation i do the following to substitute for x:
x = 400 - y
so i substitute this into my second equation:
10(400-y)+5y = 22.50
4000-10y+5y=22.50
4000+5y=22.50
-4000 -4000
5y= -3977.50
--- --------
5 5
y = -795.50
so now i substituted this answer that i got for y into my first equation:
x + y = 400
x - 795.50 = 400
+ 795.50 +795.50
x = 1195.50
am i even doing this correctly or no.what am i doing wrong and which answer will be for my white and color copies because i don't see it.
I think you have mixed the units.
x+y=400 is ok.
For the second one, you have put in 10 cents and 5 cents but used dollars for the 22.50. You should change one or the other.
I would make it
0.10x + 0.05y=22.50
then solve for x and y.
so then, that means that there are 50 copies of white and 350 of color.
right
Your initial steps in setting up the system of equations are correct. The first equation is x + y = 400, where x represents the number of white copies and y represents the number of colored copies.
However, you made a mistake in the second equation. The cost of colored copies should be 10 cents per copy, not 10 dollars. Similarly, the cost of white copies should be 5 cents per copy, not 5 dollars. Thus, the correct equation should be 0.10x + 0.05y = 22.50.
To solve for x and y, you can use the substitution method or the elimination method. Let's use the substitution method.
From the first equation, x + y = 400, we can solve for x in terms of y: x = 400 - y.
Substitute this value of x into the second equation:
0.10(400 - y) + 0.05y = 22.50.
Simplify the equation:
40 - 0.10y + 0.05y = 22.50,
40 - 0.05y = 22.50.
Rearrange the equation:
-0.05y = 22.50 - 40,
-0.05y = -17.50.
Divide both sides by -0.05:
y = (-17.50) / (-0.05),
y = 350.
Now substitute this value of y back into the first equation to find x:
x + 350 = 400,
x = 400 - 350,
x = 50.
Therefore, Sandy made 50 white copies and 350 colored copies.
So, you are correct, there are 50 copies of white and 350 of color.