THE COST OF MAKING A DRESS IS PARTLY CONSTANT AND PARTLY VARIES WITH THE AMOUT OF TIME TO MAKE D DRESS IF IT TAKES 3 HOURS TO MAKE IT COST 2700 AND TAKES 5 HOURS TO MAKE THE DRESS COST 3100 FIND THE COST IF IT TAKES 11/2HOURS TO MAKE THE DRESS
You can form 2 ordered pairs of the type (time, cost) and they are
(3, 2700) and (5, 3100)
cost = m(time) + constant
m = slope = (3100-2700)/(5-3) = 200
plug in the point (3,2700) to find the constant:
2700 = 200(3) + constant
constant = 2100
cost = 200(time) + 2100
so when t = 11/2, cost = .....
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To solve this problem, we can use the information given to form a linear equation.
Let's assume the constant cost of making the dress is represented by "C" and the variable cost that varies with the amount of time is represented by "V".
From the given information, we have two data points:
When it takes 3 hours to make the dress, the cost is $2700:
C + V(3) = 2700
When it takes 5 hours to make the dress, the cost is $3100:
C + V(5) = 3100
Now we can solve these equations simultaneously to find the values of C and V.
From the first equation:
C + 3V = 2700 --(1)
From the second equation:
C + 5V = 3100 --(2)
To isolate C, we can either multiply equation (1) by 5 and equation (2) by 3 or vice versa. Let's multiply equation (1) by 5 and equation (2) by 3:
5(C + 3V) = 5(2700)
3(C + 5V) = 3(3100)
Simplifying these equations:
5C + 15V = 13500 --(3)
3C + 15V = 9300 --(4)
Now, subtract equation (4) from equation (3):
(5C + 15V) - (3C + 15V) = 13500 - 9300
Simplifying:
5C + 15V - 3C - 15V = 4200
2C = 4200
C = 2100
Now that we have the value of C, we can substitute it into one of the original equations to solve for V. Let's use the first equation:
C + 3V = 2700
2100 + 3V = 2700
3V = 600
V = 200
Therefore, the constant cost of making the dress (C) is $2100 and the variable cost per hour of making the dress (V) is $200.
To find the cost if it takes 11/2 hours to make the dress, substitute the value into the equation:
Cost = C + V(11/2)
Cost = 2100 + 200(11/2)
Cost = 2100 + 1000
Cost = 3100
So, if it takes 11/2 hours to make the dress, the cost will be $3100.