8. Four friends throw a party for their school's basketball team. To have enough food for the whole team, each friend buys 1 medium pizza, 2 orders of breadsticks, and 1 salad. Let \( p \) represent the price of 1 medium pizza. Let \( b \) represent the price of 1 order of breadsticks. Let \( s \) represent the price of 1 salad. All prices are in dollars. a. Write two different expressions that represent the total amount of money the friends spend. Explain how each expression describes the situation in a different way. b. The party is running out of food, so another friend orders 1 medium pizza and 1 salad. Write an expression to represent the total cost of all the food after this order.
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The friends’ total spending can be expressed in two different ways. First, we can sum up their individual purchases: \( 4( p + 2b + s) \), representing each of the 4 friends buying 1 pizza, 2 breadsticks, and 1 salad. Alternatively, we can calculate the total for each food type separately: \( 4p + 8b + 4s \), showing how much they spent on pizzas, breadsticks, and salads independently, before combining them for a grand total. Both expressions provide a clear view of their overall expenditure, but from different perspectives. After the additional order, the total cost of the food will be represented by the expression \( 4( p + 2b + s) + p + s \). This combines the original expression for the four friends with the new order of 1 medium pizza and 1 salad. As a result, we now have a total expenditure reflecting all the food acquired for the party. By organizing the costs in this way, we ensure that everyone is well-fed and happy at the celebration!