Algebra 1 Help, equations/graphing?

Question

I need help with this problem, I've checked with others and I get the equation 8x+127=3464, but it graphs out to be negative which we all have a hard time believing. Im not sure if I need 2 equations or whatnot, but some help would be great :

Please use x=waxes, and y=wash-&-waxes, as thats how I tried the problem so I dont want to mix up my variables.

A car wash charges $8 per was, and $12 per wash-&-wax. After a busy day sales totalled $2464 Write an equation to represent total sales for the day in terms of washes and wash-&-waxes that could have been done that day. Then, graph your equation and give an example for the number of washes and the number of wash-&-waxes that could have been done that day to yield the given total sales.

Answer 1

The equation for this formula is:

8x+12y=2464 If we clear the "y" you will have the following straight line:

8x+12y=2464

12y=2464-8x

y=616/3 - 2/3x or y=205.33-0.66x

This is a straight line with a negative slope that intercept the "y" axis in y=616/3 or y=205.33 (when x=0) and intercepts the "x" axis in x=308 (When y=0)

And One example will be if there is 20 waxes (this mean x=20) that means that we need:

y=616/3 - 2/3(20)

y=616/3-40/3

y=576/3

y=192

192 wash&waxes to have as total sales $2464.

I hope this can be useful

David

Answer 2

I get pretty much the same thing. The equation is 8x+12y=2464. when you solve this for y you get y=(2464-8x)/12. When you graph this then your graph does come out negative. This is because there is a point for both the x value and the y value that if you exceed a certain amount then you have to take away from the other value (making it negative) to maintain your total sales. These points are the "zeros" of your equation both on the x and y axes. If you will solve the equation where y=0 and where x=0 individually you will find these points.

Answer 3

The equation is:

8x + 12y = 2464

y =  (2464 - 8x)/12 = 1/3*(616 - 2x)

as some of the other collaborators already said the slope is negative;

but that does not mean the graph is wrong.

Now, for the second part of the question; you will notice that if you give "integer" values to x; you will get integer and non integer values of y; and all values of x and y will be valid in terms of the equation; for example; if x = 1 then y = 204.6667; and 8x+12y = 2464;

BUT you can only have integer or "whole" numbers of washes and "wash and waxes"; so the non-integer values of "y" are not valid for the "real" situation.

So the only valid number of "WASHES" (x) are those numbers that will result in integer values of y.

If we go back to the eqation:

y=1/3*(616-2x)

for y to be an integer; the part in parenthesis (616-2x);

has to be divisible ( therefore a multiple) of 3;

for exaple; for x=2

616-2*(2) = 616-4 = 612; and 612/3 = 204; so if in a given day there

were only 2 washes, there has to be 204 wash and waxes; for the total sales to be 2464.

You will notice (if you use an excel spreadsheet); that starting at

2; the values of x that result in an integer value of y are one

every 3 numbers; that is 2, 5, 8, 11, 14, 17, 20 and so for; so if you increase x by 3, the "2x" part of the equation changes by 6; and that is what makes the (616-2x) become a multiple of 3; which in turn makes y integer.

Hope this helps.

Answer 4

i give up