Tim is looking at two websites that allow customers to print their own designs on T-shirts. One website charges $24 per T-shirt plus $8 shipping. The other website uses the equation [tex]C =22 n +12[/tex] to find the total cost, C, of printing n T-shirts. What is the difference in the cost of each website if Tim orders 10 T-shirts?

Question

Anonymous · Answer

The total cost for Website 1 is $248, while the total cost for Website 2 is $232. The difference in cost between the two websites when ordering 10 T-shirts is $16. Tim should choose based on this cost analysis. 
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GinnyAnswer · Answer

Calculate the total cost for Website 1: ( $24 × 10 ) + $8 = $248 . 
 Calculate the total cost for Website 2: 22 × 10 + 12 = $232 . 
 Find the difference between the total costs: $248 − $232 = $16 . 
 The difference in cost between the two websites is $16 ​ . 
 
 Explanation 
 
 Problem Analysis Let's analyze the problem. We have two websites with different pricing models for T-shirts. We need to calculate the total cost for each website when ordering 10 T-shirts and then find the difference in cost between the two websites. 
 
 Website 1 Cost Calculation First, let's calculate the total cost for Website 1. The cost per T-shirt is $24 , and the shipping cost is $8 . For 10 T-shirts, the total cost is calculated as follows: T o t a l C os t = ( C os t p er T − s hi r t × N u mb er o f T − s hi r t s ) + S hi pp in g cos t T o t a l C os t = ( $24 × 10 ) + $8 T o t a l C os t = $240 + $8 T o t a l C os t = $248 
 
 Website 2 Cost Calculation Next, let's calculate the total cost for Website 2. The equation for the total cost is given as C = 22 n + 12 , where n is the number of T-shirts. For 10 T-shirts, the total cost is calculated as follows: C = 22 n + 12 C = ( 22 × 10 ) + 12 C = 220 + 12 C = 232 
 
 Cost Difference Calculation Now, let's find the difference in cost between the two websites: D i ff ere n ce = ∣ T o t a l C os t o f W e b s i t e 1 − T o t a l C os t o f W e b s i t e 2∣ D i ff ere n ce = ∣$248 − $232∣ D i ff ere n ce = $16 
 
 Final Answer Therefore, the difference in the cost of each website if Tim orders 10 T-shirts is $16 .

Examples 
 Imagine you're planning a class trip and need to order T-shirts for all the students. Two different printing companies offer different pricing structures. By calculating the total cost from each company, just like we did in the problem, you can determine which company offers the best deal for your specific order size. This type of cost analysis is crucial in many real-life scenarios, from personal shopping to business decisions, ensuring you make the most economical choice.

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