How do I put this word problem into an equation?

Question

I believe it's a non-linear equation, but am once again stumped. A student charges $7 to wash a window. He washes 15 of them for $35. Write an equation.

Well, I've figured that the 1st window is $7 and all subsequent windows are $2 a piece. I've tried to write the equation so that when you enter a "0" for x, you would get "0," as if the student is washing "0" windows, they will get paid "0" dollars. Now, I just need to figure out how to write the equation.

The one with the most details gets the 10 points, as I am not just looking for the answer, because I want to understand what's going on.

Answer 1

I suspect that you're dealing with a linear equation here.

Since one window washed costs $7, we could take the point (1,7).
And since 15 windows washed costs $35, we could take the point (15,35).

So we need to find an equation connecting those two points, (1,7) and (15,35).

Perhaps the most common way of accomplishing this is to fill out the slope-intercept form:

y = m*x + b.

We can get the slope,

m = ( y2 - y1 ) / ( x2 - x1 )
. . = ( 35 - 7 ) / ( 15 - 1 )
. . = 28 / 14
. . = 2.

This gives our equation so-far as:

y = 2*x + b.

To find the y-intercept, b, substitute in one of the points. Since (1,7) has lower numbers, it'll probably be easiest (although both points _will_ give the same result). Thus,

(7) = 2*(1) + b
7 = 2 + b
b = 7 - 2 = 5.

So the equation for the line is

y = 2*x + 5.

We can check this equation against our points (1,7) and (15,35) to see that it does hold.

And, conceptually, it does make sense. Each window is worth a certain amount, plus a fee to get to the job.

Answer 2

If the student charges $7 for the first window, the remaining 14 cost $28, or $2 each, like you said.

Since the student gets paid the same amount for each window washed (except the first one), the equation must be linear, meaning that it's impossible to use the point (0,0) in the graph.

That being said, the equation needs to be set up using a restricted domain, in this case any value of x greater than or equal to 1 (the lowest number of windows the student would be paid to wash). The domain also can't include anything except for whole numbers because the student won't wash part of a window.

In the restricted domain, the student will always get $7 (for the first window), so that will be part of the constant value in the equation. The $2 for each window afterwards is the amount that varies, so that will be the coefficient of x in the equation. The $2 for each extra window is multiplied by the total number of windows the student washed except for the first one and added to $7 to find the total amount of money, so the $2 has to be multiplied by (x-1).

This yeilds the equation y = 2(x-1) +7, which can be simlified to y = 2x +5 for the restricted domain of {x|x belongs to integers and x is greater than or equal to 1}.

Answer 3

If the student charges $7 for the first window and then $2 for every additional window, then you could write your equation as follows (D = Dollars, W = Windows):

D = 2W + 5 for all W > 0, and D = 0 where W = 0.

If you put in 1 for W, you end up with your $7 for the first window, and 15 windows would yield $35.

Answer 4

If he charges $7 per window, he cannot wash 15 windows for $35. But if you are changing the problem to be that he washes the 1st window for $7 and each susequent window for $2, then total charge is
C = 7n {n=0 or 1}
C= 7+2n {n>1}

This allows your requirement that washing zero windows results in zero cost. The above answers do not respon to that requirement and give equations indicating he gets $5 for washing 0 windows.

Answer 5

Let T = total

T = $7 + (x - 1) times $2, where x is the number of windows and x must be a positive integer > 0.

Answer 6

On 8 you may % your variable to be the bracelet value because of the fact the necklace value is defined utilizing the bracelet: b = bracelet value 3b = necklace b + 3b = 192 then do like your occasion. On 9 % the variable for Junior for the reason that Grandpa is defined utilizing Junior. j = junior's age 6j - 6 = Gramps so j + 6j - 6 = seventy 8 7j - 6 = seventy 8 7j = eighty 4 j = eighty 4 ÷ 7 j = 12 so grampa is 72 - 6 = sixty six On 10 % the variable to be the 2nd action picture because of the fact the 1st is defined utilizing the 2nd. s = length of 2nd action picture 2s - 3 = length of first s + 2s - 3 = 132 3s - 3 = 132 3s = a hundred thirty five s = a hundred thirty five ÷ 3 s = 40 5 so the long is ninety - 3 = 87 min.

Answer 7

Price = 7 +2(n-1) for n > or = 1
Price = 0 for n < 1
n can only be whole numbers, so this is a step equation

This is not a linear equation! It looks linear, but because n can only be whole numbers, it is not linear.

Answer 8

x = fee per additional window
35 = 7 + x(15 - 1)
35 = 7 + 14x
28 = 14x
2 = x

Equation expressing the fee charged for window washing...
W = Number of windows
f(W) = 7 + 2(W - 1) where the domain = [1 , infinity)

Answer 9

The answer is y=2x+5, where y is the income and x is the number of windows washed.

x y=2x+5
1 7
2 9
3 11
4 13
5 15
6 17
7 19
8 21
9 23
10 25
11 27
12 29
13 31
14 33
15 35

Answer 10

I _guess_ the equation you want is one that shows how much the student charges for a job, as a function of how many windows there are. Right?

I would say it's:

cost = 7 + 2(w-1)