At a food truck, the cost in dollars of deluxe tacos and standard tacos can be modeled by the equation . If a customer orders exactly deluxe tacos, how many standard tacos can the customer also purchase for dollars in total?
A two-variable linear equation ties two item counts to one total cost. If one count is given, substitute it, subtract its cost, and solve the remaining equation with a Desmos regression. The terms are separate parts of the same bill, so dividing the cost already spent by the other item's price counts the wrong money.
Hints
- Hint 1
A coefficient is the number multiplying a letter. Here, is the price of one deluxe taco. The customer orders three deluxe tacos, so what number replaces in the equation?
- Hint 2
Each term of the equation is part of the total bill. The deluxe tacos are already included in the $27, so subtract their cost to leave , the cost of all the standard tacos.
Step-by-step
Subtract the known cost, then solve
Step 1Substitute the deluxe-taco count
The equation adds the costs of the two kinds of tacos. The customer orders three deluxe tacos, so put in for : . Here, is the deluxe-taco cost, and is the standard-taco cost.
- Step 2
Leave only the standard-taco cost
The deluxe-taco cost is already part of the $27 total. Subtract from both sides: . Subtract the known items' cost before finding how many of the other item you can buy.
- Step 3
Find the number of standard tacos
Type in Desmos. The tells Desmos to find the value of that makes the costs match. Under PARAMETERS, it shows . So the customer can buy 10 standard tacos along with the three deluxe tacos for $27. Choice C.