To write an equation for the given situation, we really need to think about each factor that goes into the calculation of our total cost.

Total Cost and Tip

The total cost is

$ 13.80,

the

$ 3

tip is a constant added after the tax and ordered items are already taken into consideration.

\dots + 3 = 13.80

Food Purchased

Let the unknown cost of a taco be

t .

We can write an expression for the ordered items, two tacos and a salad, using the fact that the salad is known to be

$ 2.50 .

2 t + 2.50

Sales Tax

To account for sales tax, we need to use the percent change in the total cost. The sales tax is

8 %

so the total cost of the meal is going to be

8 %

higher.

100 % + 8 % = 108 %

We can multiply the cost of the meal by this percent change. However, for simplicity, let's think about this in the decimal format rather than as a percentage,

108 % = 1.08 .

Final Equation

Now, we can combine all of the components of the bill to have an equation that we can solve for the cost of tacos.

Sales tax \times (Food cost) + Tip = Total cost 1.08 (2 t + 2.50) + 3 = 13.80

Let's solve the equation for

t

to find the cost of each taco.

1.08 (2 t + 2.50) + 3 = 13.80

SubEqn

$LHS - 3 = RHS - 3$

1.08 (2 t + 2.50) = 10.80

DivEqn

$LHS / 1.08 = RHS / 1.08$

2 t + 2.50 = 10

SubEqn

$LHS - 2.50 = RHS - 2.50$

2 t = 7.50

DivEqn

$LHS / 2 = RHS / 2$

t = 3.75

Each taco costs

$ 3.75 .

Exercise