The taxi fare in Gotham City is $2.40 for the first ½ mile and additional mileage is charged at the rate of $0.20 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $10?
What are two different ways you can solve this problem?
In Arithmetic form.
10 - 2 = 2.40 + 0.20 m
To solve this problem, we can use two different methods: arithmetic and algebra.
1. Using Arithmetic:
Step 1: Deduct the tip amount from the total budget ($10 - $2 = $8).
Step 2: Calculate the cost of the first 0.5 miles: $2.40.
Step 3: Calculate the cost of each additional 0.1 mile: $0.20.
Step 4: Determine the number of additional 0.1 miles that can be covered within the remaining budget.
Remaining budget / Cost per additional 0.1 mile
$8 / $0.20 = 40
Step 5: Calculate the total distance
(0.5 miles) + (40 * 0.1 miles)
0.5 + 4
4.5 miles
Thus, you can ride for a total of 4.5 miles with a $10 budget.
2. Using Algebra:
Let's assume the number of additional 0.1 miles is represented by 'x.'
The cost of the first 0.5 miles is $2.40.
The cost of additional miles is given by the equation: $0.20 * x.
The total cost can be expressed as the sum of the cost of the first 0.5 miles and the cost of additional miles:
Total cost = $2.40 + $0.20x.
We know that the budget is $10, which means the total cost cannot exceed $10:
$2.40 + $0.20x ≤ $10.
Now, we can solve the inequality to find the maximum value of 'x':
$0.20x ≤ $10 - $2.40
$0.20x ≤ $7.60
x ≤ $7.60 / $0.20
x ≤ 38.
Since the value of 'x' represents the number of additional 0.1 miles, we can calculate the total distance:
Total distance = (0.5 miles) + (x * 0.1 miles)
Total distance = 0.5 + 3.8
Total distance = 4.3 miles.
So, according to the algebraic method, you can ride for a total of 4.3 miles with a $10 budget.
To solve this problem in arithmetic form, we can use two different methods: the equation method and the table method.
1. Equation Method:
Let's assume the number of additional 0.1 miles you ride is x.
The total cost for the additional mileage can be calculated using the formula:
Additional mileage cost = 0.20 * x
Adding the initial fare of $2.40 to the additional mileage cost, we can write:
Total cost = 2.40 + (0.20 * x)
We also want to leave a $2 tip, so:
Total cost + Tip = 10
(2.40 + 0.20x) + 2 = 10
Now let's solve this equation to find the value of x:
2.40 + 0.20x + 2 = 10
0.20x + 4.40 = 10
0.20x = 10 - 4.40
0.20x = 5.60
x = 5.60 / 0.20
x = 28
Therefore, you can ride for an additional 28 * 0.1 = 2.8 miles.
2. Table Method:
Create a table to list the cost for different numbers of additional 0.1 miles.
Number of additional 0.1 miles (x) | Additional mileage cost (0.20 * x)
--------------------------------------------------------------
0 | 0 * 0.20 = 0
1 | 1 * 0.20 = 0.20
2 | 2 * 0.20 = 0.40
3 | 3 * 0.20 = 0.60
... | ...
28 | 28 * 0.20 = 5.60
The total cost (including the initial fare and tip) is $10.
Let's fill in the table:
Number of additional 0.1 miles (x) | Additional mileage cost (0.20 * x) | Total cost (including initial fare and tip)
---------------------------------------------------------------------------------------------------------------------------------
0 | 0 * 0.20 = 0 | 2.40 + 0 + 2 = 4.40
1 | 1 * 0.20 = 0.20 | 2.40 + 0.20 + 2 = 4.60
2 | 2 * 0.20 = 0.40 | 2.40 + 0.40 + 2 = 4.80
...
28 | 28 * 0.20 = 5.60 | 2.40 + 5.60 + 2 = 10
From the table, we can see that when the number of additional 0.1 miles is 28, the total cost is exactly $10.
Therefore, you can ride for an additional 28 * 0.1 = 2.8 miles for $10.