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QuestionYou buy 2 tacos and a salad for \$13.60. The salad is \$2.50, plus 6% tax and a \$3 tip. Find the cost of one taco.

Studdy Solution

STEP 1

Assumptions1. The cost of the salad is .50.Thesalestaxrateis6.50. The sales tax rate is6%<br />3. The tip amount is 34. The total amount paid is $13.605. The sales tax is applied to the total cost of the food (tacos and salad), not the tip6. The cost of two tacos is the same, i.e., each taco costs the same amount

STEP 2

We need to find an equation that represents the total cost. The total cost is the sum of the cost of the food, the sales tax on the food, and the tip.
Total cost=Cost of food+Sales tax+TipTotal\, cost = Cost\, of\, food + Sales\, tax + Tip

STEP 3

The cost of the food is the sum of the cost of the salad and the cost of two tacos. Let's represent the cost of one taco as tt.
Cost of food=Cost of salad+2timesCost of one tacoCost\, of\, food = Cost\, of\, salad +2 \\times Cost\, of\, one\, tacoCost of food=$2.50+2tCost\, of\, food = \$2.50 +2t

STEP 4

The sales tax is calculated as a percentage of the cost of the food.Sales tax=Sales tax ratetimesCost of foodSales\, tax = Sales\, tax\, rate \\times Cost\, of\, foodSales tax=0.06times($2.50+2t)Sales\, tax =0.06 \\times (\$2.50 +2t)

STEP 5

Now we can substitute the expressions for the cost of food and sales tax back into the equation for the total cost.
Total cost=$2.50+2t+0.06($2.50+2t)+$3Total\, cost = \$2.50 +2t +0.06(\$2.50 +2t) + \$3

STEP 6

We know that the total cost is $13.60. We can set our equation equal to this amount to find the cost of one taco.
$2.50+2t+0.06($2.50+2t)+$3=$13.60\$2.50 +2t +0.06(\$2.50 +2t) + \$3 = \$13.60

STEP 7

implify the equation by distributing the sales tax rate through the parentheses.
$2.50+2t+$0.15+0.12t+$3=$13.60\$2.50 +2t + \$0.15 +0.12t + \$3 = \$13.60

STEP 8

Combine like terms.
2.12t+$5.65=$13.602.12t + \$5.65 = \$13.60

STEP 9

Subtract 5.65frombothsidesoftheequationtoisolatethetermwith5.65 from both sides of the equation to isolate the term with t$.
2.12t=$13.60−$5.652.12t = \$13.60 - \$5.65

STEP 10

Perform the subtraction on the right side of the equation.
2.12t=$7.952.12t = \$7.95

STEP 11

Finally, divide both sides of the equation by .. to solve for tt, the cost of one taco.
t=$7.95/.t = \$7.95 /.

STEP 12

Perform the division on the right side of the equation.
t=$.75t = \$.75One taco costs $.75.

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