Fred bought a large pizza for $\$18.00$. Toppings, $t$, cost $\$2.00$ each. He used a coupon for $\$4.00$ off. Write an expression to show how much Fred would have to pay if he adds on 3 toppings.
The problem involves determining the total cost of a pizza based on a base price, a variable cost per topping, and a fixed discount. We are given:
To find the cost for any number of toppings \(t\), we represent the cost as a function \(C(t)\) by adding the base price to the total cost of the toppings and then subtracting the discount:
\[C(t) = 18 + 2t - 4\]
To find the specific cost for \(3\) toppings, we substitute \(t = 3\) into our expression:
\[C(3) = 18 + 2(3) - 4\]
First, we calculate the cost of the toppings: \(2 \times 3 = 6\).
Next, we add the base price and the topping cost: \(18 + 6 = 24\).
Finally, we apply the coupon discount: \(24 - 4 = 20\).
Thus, the cost for a pizza with \(3\) toppings is \(\$20.00\).
Understanding how to build an algebraic expression for pricing is essential for everyday tasks, such as budgeting for meals or calculating discounts while shopping. For example, if you are ordering a subscription service with a monthly fee plus variable costs for extra storage, you can write a similar expression to track your monthly expenses accurately. This skill allows you to evaluate total costs quickly and plan your spending effectively.