X= price of hotdog
y= price of hamburger
Set up equations for each stand. Multiply number of hotdogs and hamburgers sold by their prices (x and y) and add together to equal the total sold at each stand.
FIRST CONCESSION STAND
164x + 74y= $706
SECOND CONCESSION STAND
256x + 61y= $884
STEP 1
to solve by elimination, multiply first concession stand equation by 61; this will eliminate the y term
164x + 74y= $706
(61)(164x) + (61)(74y)= (61)(706)
10,004x + 4,514y= 43,066
STEP 2
multiply second concession stand equation by -74
256x + 61y= $884
(-74)(256x) + (-74)(61y)= (-74)($884)
-18,944x - 4,514y= -65,416
STEP 3
add step 1 & 2 equations together to solve for x
10,004x + 4,514y= 43,066
-18,944x - 4,514y= -65,416
y terms "cancel out"
-8,940x= -22,350
divide both sides by -8,940
x= $2.50 hotdog
ANSWER: $2.50 is the price of a hotdog.
Hope this helps! :)
The answer is 9.3, divide the distance between town A&B by the speed of the automobile. 420/45= 9.3 hours.
Hi! I'm happy to help!
Point slope form states that y-
=m(x-
). m represents your slope (rise/run) and and represent your first y and x points, and y and x represent your second y and x points. We already have our equation here:
y - 4 = 1/4(x- 8)
Now, let's dive into what slope-intercept form is. Slope intercept form states that y=mx+b. m represents our slope, b represents our y intercept, y represents a y point, and x represents the corresponding x point.
Since we know our m, we can solve for b, by using our other numbers. Let's use our first set of coordinates.
4=1/4(8)+b
4=2+b
2=b
Now our second set to double check:
2=1/4(0)+b
2=0+b
2=b
We know that b must equal 2, so our equation must be y=1/4x+2, which is option 3.
<u>You should pick option 3.</u>
<u>(y-intercept is where the line hits the y-axis(when x=0). We could've used our second coordinates (0,2), where x equals 0 to know that 2 is the y-intercept (b). This shortcut only works on specific problems though.)</u>
I hope this was helpful, keep learning! :D
Answer:
The maximum profit of $ 10277.32____ can be made when the selling price of the dog food is set to $ _34___ per bag.
Step-by-step explanation:
Profit = Revenue - Cost
P(x) = R(x) -C(x)
= -31.72x^2 + 2,030x
-( -126.96x + 26,391)
Distribute the minus sign
= -31.72x^2 + 2,030x+126.96x - 26,391
Combine like terms
= -31.72 x^2 + 2156.96 x - 26391
This is a parabola. It is facing downwards. The maximum profits is at the vertex ( where the max is)
vertex = h = -b/2a = -(2156.96)/(2*-31.72) = -2156.96/-63.44=34
Evaluate P(x) at x=34 to determine the profit
P(34) = -31.72 (34)^2 + 2156.96 (34) - 26391
-36668.32+73336.64-26391
10277.32
