Aclothing store spends $15 for each sweatshirt it produces and has fixed
costs of $600. if the store makes 60 sweatshirts, how much should the store
charge for each sweatshirt in order to break even?

The cost of each sweatshirt in order to break even is $25

Step-by-step explanation:

Given as :

The amount that store spend on each sweatshirt = $15

The fixed cost for production = $600

The total number of sweatshirt that store makes = 60

Let The price of each sweatshirt = $A

Now, According to question

∵ each sweatshirt cost $15 , and number of shirt made is 60

∴ The money spend on making 60 shirts = $15 × 60

i.e The money spend on making 60 shirts = $900

Again

The fixed cost for production = $600

So,Total money spend on shirt making = fixed cost  + price on making 60 shirts

i.e Total money spend on shirt making = $600 + $900

Or, Total money spend on shirt making = $1500

Again

The price of each sweatshirt =

Or, A =

∴  Amount = $25

So, The cost of each sweatshirt = A = $25

Hence, The cost of each sweatshirt in order to break even is $25 . Answer

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

slope is 35 and 20 miles is the y-intercept.

step-by-step explanation: