The cost of buying is partly constant and partly varies with number of shirt bought when the number of shirt is 5, the cost is 240, also ten shirt cost is 400 find the cost when 300 shirt were bought
cost = a + bs, where a and b are constants, and s is the number of shirts.
a + 5b = 240
a + 10b = 400
I would subtract them, get b, and then a
you now have the full equation,
find cost when s = 300
c = cost
n =number
then
c = m * n + b
-----------------------
240 = 5 m + b
400 =10 m + b
--------------------- subtract
- 160 = - 5 m
m = 32
so c = 32 n + b
400 = 32 (10) + b
b = 80
so
c = 32 n + 80
if n = 300
c = 32 * (300) + 80
Well, if ten shirts cost 400, that means each shirt costs 40 (400 divided by 10). And if the cost is partly constant, then we can assume that the constant cost is 40, since that's the cost per shirt when ten are bought.
Now, since the cost also varies with the number of shirts, we need to find out how much the cost varies. We can do this by looking at the difference in cost when the number of shirts changes.
When the number of shirts goes from 5 to 10, the cost goes from 240 to 400. That's an increase of 160 (400 - 240). And since the cost varies with the number of shirts, we can assume that the cost increases by 160 for every 5 shirts.
So, for every 5 shirts, the cost increases by 160.
Now, if we want to find the cost when 300 shirts are bought, we need to figure out how many groups of 5 shirts are in 300.
300 divided by 5 is 60. So, there are 60 groups of 5 shirts in 300.
And since the cost increases by 160 for each group of 5 shirts, we can multiply 160 by 60 to get the total increase in cost.
160 times 60 is 9600. So, the cost increases by 9600 when 300 shirts are bought.
Now, we need to add the constant cost of 40 to the increased cost of 9600.
40 plus 9600 is 9640.
Therefore, the cost when 300 shirts are bought is 9640.
Hope that helps!
To find the cost when 300 shirts were bought, we need to determine the constant part of the cost and the part that varies with the number of shirts.
We are given that when 5 shirts are bought, the cost is $240. This gives us one equation:
5 shirts = $240
Next, we are given that 10 shirts cost $400. This gives us another equation:
10 shirts = $400
We can use these two equations to find the constant part of the cost and the part that varies with the number of shirts.
First, we need to find the cost per shirt when 5 shirts are bought:
Cost per shirt = Total cost / Number of shirts
Cost per shirt = $240 / 5 = $48
Now, we can find the constant part of the cost by subtracting the part that varies from the total cost.
Constant part of the cost = Total cost - (Cost per shirt * Number of shirts)
Constant part of the cost = $240 - ($48 * 5) = $240 - $240 = $0
Since the constant part of the cost is $0, it means that the cost only varies with the number of shirts.
Now, we can find the cost when 300 shirts were bought using the cost per shirt we calculated earlier:
Cost when 300 shirts were bought = Cost per shirt * Number of shirts
Cost when 300 shirts were bought = $48 * 300 = $14,400
Therefore, the cost when 300 shirts were bought is $14,400.