let number of t-shirts be t
3.5t + 30 = 2.5t + 50
solve for t
· Company A charges $50 to set up the artwork.
· Company B charges $30 to set up the artwork.
· Company A charges $2.50 per shirt.
· Company B charges $3.50 per shirt.
How many shirts would need to be printed for Company A’s total cost to be equivalent to Company B’s total cost?
3.5t + 30 = 2.5t + 50
solve for t
Let's assume the number of shirts to be printed is represented by 'x'.
For Company A:
Total cost = (cost per shirt * number of shirts) + setup cost
Total cost = (2.50 * x) + 50
For Company B:
Total cost = (cost per shirt * number of shirts) + setup cost
Total cost = (3.50 * x) + 30
Since we want the total costs to be equal, we can set the two equations equal to each other and solve for 'x':
(2.50 * x) + 50 = (3.50 * x) + 30
Subtract 2.50x and 30 from both sides:
20 = 1.00x
Divide both sides by 1.00:
x = 20
Therefore, 20 shirts would need to be printed for Company A's total cost to be equivalent to Company B's total cost.
For Company A, the total cost includes the setup fee ($50) plus the cost per shirt ($2.50) multiplied by the number of shirts (x). So, the total cost for Company A would be 50 + 2.50x.
For Company B, the total cost includes the setup fee ($30) plus the cost per shirt ($3.50) multiplied by the number of shirts (x). So, the total cost for Company B would be 30 + 3.50x.
To find the number of shirts that would make the total cost for both companies equal, we can set up the equation:
50 + 2.50x = 30 + 3.50x
Now, we can solve this equation to find the value of "x".
Subtracting 2.50x from both sides:
50 = 30 + 3.50x - 2.50x
Combining like terms:
50 = 30 + 1x
Subtracting 30 from both sides:
20 = 1x
Dividing both sides by 1:
x = 20
Therefore, 20 shirts would need to be printed for Company A’s total cost to be equivalent to Company B’s total cost.