Citydog Screen Printers received two orders for a t-shirt designed for a math symposium. The first order was for 40 shirts at a total cost of $295 and the second order was for an additional 80 shirts at a total cost of $565. Each order included a shipping and handling charge.

Then we have to writer a linear equation, for which I got: y-27/4x+25. We also had to find the cost per t-shirt, for which I got: $31.75. The last part I don't understand, however: fidn the shipping and handling charge.

If anyone could help, I would really appreciate it. Thanks in advance.

The second word problem is:
It costs Consolidated Cereals Corporation $1050 to produce 100 boxes of corn flakes and $1250 to produce 500 boxes. I found the cost function: c(x)=1/2x+1000 but don't know how to determine the fixed cost and the variable cost per box (mainly because I have no idea what those are.)

Once again, thanks in advance.

I don't agree with your solution to the first question.

Cost= m x+b

x is the cost per shirt, b is the handling charge

295=40m+b
565=80m+b
subtract the first equation from the second:
370=40x solve for m, the cost of each shirt. Then solve for b, put all that into y= mx+b
One the second question,
Cost= variable cost * n + Fixedcosts or
cost= n*v+F

1250=500v+f
1050=100v+f
subtract the second equation from the first
200=400v solve for v, and it is 1/2 dollar. Solve for f, the fixed cost, and it looks as if it is 1000 dollars.

Thanks for your help, but my teacher wanted me to use point-slope form to solve the equations rather than subtracting one equation from the other. Do you know how to do that?

To find the shipping and handling charge for the t-shirt orders, we need to first find the cost per shirt for each order, and then subtract that from the total cost of the order. Let's break it down step by step:

1. First Order:
The first order was for 40 shirts at a total cost of $295. To find the cost per shirt, divide the total cost by the number of shirts:
Cost per shirt = Total cost / Number of shirts = $295 / 40 = $7.375

2. Second Order:
The second order was for an additional 80 shirts at a total cost of $565. Similarly, divide the total cost by the number of shirts to find the cost per shirt:
Cost per shirt = Total cost / Number of shirts = $565 / 80 = $7.0625

3. Shipping and Handling Charge:
To find the shipping and handling charge, we need to find the additional cost that is not accounted for by the cost per shirt. Subtract the cost per shirt calculated in step 1 or 2 from the total cost of the order:

Shipping and handling charge for the first order = Total cost of the first order - Total cost of shirts in the first order
Shipping and handling charge for the first order = $295 - ($7.375 * 40)
Shipping and handling charge for the first order = $295 - $295
Shipping and handling charge for the first order = $0

Shipping and handling charge for the second order = Total cost of the second order - Total cost of shirts in the second order
Shipping and handling charge for the second order = $565 - ($7.0625 * 80)
Shipping and handling charge for the second order = $565 - $566
Shipping and handling charge for the second order = -$1

Based on the calculations, the shipping and handling charge for the first order is $0, and the shipping and handling charge for the second order is -$1. It seems like there might be an error or inconsistency in the given data, as a negative shipping and handling charge is not possible. You may want to double-check the information to get accurate results.

Moving on to the next problem:

To determine the fixed cost and variable cost per box for producing corn flakes, we can use the cost function equation you provided: c(x) = 1/2x + 1000.

In this equation, "x" represents the number of boxes of corn flakes being produced, and "c(x)" represents the total cost of production.

1. Variable Cost per Box:
The coefficient of "x" in the equation represents the variable cost per box. In this case, the coefficient is 1/2. Therefore, the variable cost per box is $0.50.

2. Fixed Cost:
The constant term in the equation represents the fixed cost. In this case, the constant term is 1000. Therefore, the fixed cost is $1000.

To summarize:
- Variable cost per box: $0.50
- Fixed cost: $1000