To determine which expression represents the total cost of all the pizzas the softball team orders, let's break down the cost for each type of pizza:
1. Cost of cheese pizzas: Each cheese pizza costs [tex]$6. If the team orders \( c \) cheese pizzas, the total cost for cheese pizzas would be:
\[
6c
\]
2. Cost of four-topping pizzas: Each four-topping pizza costs $[/tex]10. If the team orders [tex]\( f \)[/tex] four-topping pizzas, the total cost for four-topping pizzas would be:
[tex]\[
10f
\][/tex]
Next, to find the total cost of all the pizzas, we sum the cost of the cheese pizzas and the four-topping pizzas:
[tex]\[
6c + 10f
\][/tex]
Now, let's examine the given options:
- (A.) [tex]$6 + 10$[/tex] — This option simply adds the price of one cheese pizza and one four-topping pizza without considering the quantities [tex]\( c \)[/tex] and [tex]\( f \)[/tex]. It does not represent the total cost based on the number of pizzas ordered.
- (B.) [tex]$c + f$[/tex] — This option adds the number of cheese pizzas and the number of four-topping pizzas without considering their respective prices. It does not reflect the total cost either.
- (C.) [tex]$6c + 10f$[/tex] — This option represents the total cost correctly. It multiplies the number of cheese pizzas by [tex]$6 and the number of four-topping pizzas by $[/tex]10, then sums these costs.
- (D.) [tex]$6f + 10c$[/tex] — This option swaps the roles of [tex]\( c \)[/tex] and [tex]\( f \)[/tex]. It represents the cost incorrectly by multiplying the number of four-topping pizzas by [tex]$6 and the number of cheese pizzas by $[/tex]10.
Therefore, the correct expression that represents the total cost of all the pizzas ordered by the softball team is:
(C.) [tex]$6c + 10f$[/tex]
So, the correct option is C.
