Math  /  Algebra

Question6 A 6B 6 C 6D 6E6 E 6F 6 G 6H 61 6 J 6 K 6L
The taxi journey had an initial charge of £4£ 4 plus a cost of £2£ 2 for every kilometre travelled. a) Chloe says they should split the total cost in the same ratio as the distance each person travelled. If they did this, how much would they each pay? b) Nadia says they should split the initial charge equally and then split the rest of the cost in the same ratio as the distance each person travelled. If they did this, how much would they each pay? c) Chloe then says that she should pay nothing because the taxi was passing her house on the way to Nadia's house. Do you agree with this? Write a sentence to explain your answer.
Nadia's house
12 km Previous Watch video Answer

Studdy Solution

STEP 1

What is this asking? Two friends took a taxi and need to figure out a fair way to split the fare based on the distance each of them traveled. Watch out! Don't forget about the initial $4\$4 charge!
It needs to be included in the total cost.

STEP 2

1. Calculate the total distance.
2. Calculate the total cost.
3. Calculate Chloe's share (method 1).
4. Calculate Nadia's share (method 1).
5. Calculate Chloe's share (method 2).
6. Calculate Nadia's share (method 2).
7. Address Chloe's final statement.

STEP 3

The trip from the shop to Chloe's house is 4 km\mathbf{4 \text{ km}}.
From Chloe's house to Nadia's house is 12 km\mathbf{12 \text{ km}}.
The total distance is the sum of these two distances.

STEP 4

Total Distance=4 km+12 km=16 km \text{Total Distance} = 4 \text{ km} + 12 \text{ km} = \mathbf{16 \text{ km}} So, the taxi traveled a total of **16 km**.

STEP 5

The initial charge is $4\$\mathbf{4}.
The cost per kilometer is $2\$\mathbf{2}.
The total cost is the initial charge plus the cost per kilometer multiplied by the total distance.

STEP 6

Total Cost=$4+$216=$4+$32=$36 \text{Total Cost} = \$4 + \$2 \cdot 16 = \$4 + \$32 = \$\mathbf{36} The total cost of the taxi ride is $36\$\mathbf{36}.

STEP 7

Chloe traveled 4 km\mathbf{4 \text{ km}} out of the total 16 km\mathbf{16 \text{ km}}.
This means she traveled 416=14 \frac{4}{16} = \frac{1}{4} of the total distance.

STEP 8

If they split the cost based on the distance traveled, Chloe's share is 14 \frac{1}{4} of the total cost.

STEP 9

Chloe’s Share=14$36=$9 \text{Chloe's Share} = \frac{1}{4} \cdot \$36 = \$\mathbf{9} So, Chloe would pay $9\$\mathbf{9} using this method.

STEP 10

Nadia traveled 12 km\mathbf{12 \text{ km}} out of 16 km\mathbf{16 \text{ km}}, which is 1216=34 \frac{12}{16} = \frac{3}{4} of the total distance.

STEP 11

Nadia’s Share=34$36=$27 \text{Nadia's Share} = \frac{3}{4} \cdot \$36 = \$\mathbf{27} Nadia would pay $27\$\mathbf{27} using this method.

STEP 12

They split the initial $4\$4 equally, so each pays $42=$2\$\frac{4}{2} = \$2.

STEP 13

The remaining cost is $36$4=$32\$36 - \$4 = \$32.
Chloe's share of this remaining cost, based on the distance, is still 14 \frac{1}{4} .

STEP 14

Chloe’s Share=$2+14$32=$2+$8=$10 \text{Chloe's Share} = \$2 + \frac{1}{4} \cdot \$32 = \$2 + \$8 = \$\mathbf{10} Chloe would pay $10\$\mathbf{10} using this method.

STEP 15

Nadia also pays $2\$2 from the initial charge.
Her share of the remaining $32\$32 is 34 \frac{3}{4} .

STEP 16

Nadia’s Share=$2+34$32=$2+$24=$26 \text{Nadia's Share} = \$2 + \frac{3}{4} \cdot \$32 = \$2 + \$24 = \$\mathbf{26} Nadia would pay $26\$\mathbf{26} using this method.

STEP 17

No, I don't agree.
Even though the taxi was already going in Chloe's direction, she still benefited from the ride and should contribute to the cost.
The taxi still had to drive the initial 44 km to pick her up, and she rode in the taxi for the entire journey.

STEP 18

a) Chloe would pay $9\$9, and Nadia would pay $27\$27. b) Chloe would pay $10\$10, and Nadia would pay $26\$26. c) Chloe should still pay because she benefited from the ride, even if the taxi was already going in her direction.

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