Bort wants to make money selling tacos. He sells 25 tacos on the first day. He then sells 12 tacos each day after that.
a) Write an explicit formula to model this situation.
b) If each taco sells for $3, how much money does he make in the first 30 days? Explain how you got your answer.
Reminder: You will be graded for showing the correct process as well as the correct answer using algebraic work.
a) Let \(n\) represent the number of days Bort has been selling tacos. The number of tacos he sells on day \(n\) can be represented by the formula \(25 + 12(n-1)\).
b) To find out how much money Bort makes in the first 30 days, we first need to find out how many tacos he sells in those 30 days. We can plug in \(n = 30\) into our formula:
\(25 + 12(30-1) = 25 + 12(29) = 25 + 348 = 373\).
So, Bort sells 373 tacos in the first 30 days.
Now, we can find out how much money he makes by multiplying the number of tacos sold by the price of each taco:
\(373 \times $3 = $1119\).
Therefore, Bort makes $1119 in the first 30 days selling tacos.