# You and a friend want to start a business and design t-shirts. You decide to sell your shirts for \$1

Discussion in 'Calculator Requests' started by math_celebrity, Jul 24, 2018.

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You and a friend want to start a business and design t-shirts. You decide to sell your shirts for \$15 each and you paid \$6.50 a piece plus a \$50 set-up fee and \$25 for shipping. How many shirts do you have to sell to break even? Round to the nearest whole number.

Step 1: Calculate Your Cost Function C(s) where s is the number of t-shirts
C(s) = Cost per Shirt * (s) Shirts + Set-up Fee + Shipping
C(s) = \$6.50s + \$50 + \$25
C(s) = \$6.50s + 75

Step 2: Calculate Your Revenue Function R(s) where s is the number of t-shirts
R(s) = Price Per Shirt * (s) Shirts
R(s) = \$15s

Step 3: Calculate Break-Even Point
Break Even is where Cost = Revenue. Set C(s) = R(s)
\$6.50s + 75 = \$15s

Step 4: Subtract 6.5s from each side
8.50s = 75

Step 5: Solve for s
Run this through our equation calculator to get s = 8.824. We round up to the next integer to get s = 9.

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Last edited: Jul 24, 2018