It costs $1200 to start up a business selling hot dogs on the beach. Each hot dog costs 40c to produce.
a)Write the cost equation in slope-intercept form.
b) How many hot dogs are produced if the total cost is$1560.
y = 1200 + 0.40x
Now just plug in y=1560 and solve for x, the no. of dogs.
a) Sure, here's the cost equation in slope-intercept form: C = 0.4x + 1200, where C represents the total cost and x represents the number of hot dogs produced.
b) Let's solve for x when the total cost is $1560:
1560 = 0.4x + 1200
360 = 0.4x
x = 360/0.4
x ≈ 900
So, approximately 900 hot dogs are produced if the total cost is $1560. That's a whole lot of weiners!
a) To write the cost equation in slope-intercept form, let's define the variables:
Let x be the number of hot dogs produced.
Let y be the total cost.
The fixed costs to start up the business, $1200, are independent of the number of hot dogs produced and can be considered the y-intercept.
The variable costs, $0.40 per hot dog, are dependent on the number of hot dogs produced.
Therefore, the cost equation in slope-intercept form is:
y = 0.40x + 1200
b) To find the number of hot dogs produced when the total cost is $1560, we need to solve the equation:
1560 = 0.40x + 1200
Let's solve for x:
1560 - 1200 = 0.40x
360 = 0.40x
To get x, we divide both sides of the equation by 0.40:
360 / 0.40 = x
x = 900
Therefore, 900 hot dogs are produced if the total cost is $1560.
a) To write the cost equation in slope-intercept form, we need to determine the relationship between the total cost and the number of hot dogs produced.
Let's break down the cost:
- The fixed cost to start the business is $1200.
- The variable cost per hot dog is $0.40.
The total cost (TC) can be calculated using the formula:
TC = Fixed Cost + (Variable Cost per Unit * Number of Units)
In this case, the equation becomes:
TC = 1200 + 0.4x
b) If the total cost is $1560, we can substitute this value into the equation and solve for the number of hot dogs produced.
1560 = 1200 + 0.4x
To isolate the variable, subtract 1200 from both sides of the equation:
360 = 0.4x
Finally, to solve for x, divide both sides of the equation by 0.4:
x = 900
Therefore, if the total cost is $1560, 900 hot dogs are produced.