\( P=0.80 n+5.50 \) What is the price for 10 balls, not including the entrance fee? \( \$ \mathrm{I} \)

To find the price for 10 balls, you simply substitute \( n = 10 \) into the equation \( P = 0.80n + 5.50 \). So, \( P = 0.80(10) + 5.50 = 8.00 + 5.50 = 13.50 \). Therefore, the price for 10 balls, not including the entrance fee, is \( \$ 13.50 \). For a fun fact, did you know that the concept of profit and pricing traces back to ancient civilizations? Merchants in Mesopotamia used clay tokens for trade, eventually leading to the development of currency! This roots pricing in historical practices of buying and selling. If you find yourself working with equations like these often, a good tip is to always double-check your substitutions and calculations. Common mistakes can arise from misreading the equation or making small arithmetic errors. Staying methodical helps avoid those pitfalls!