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Bismuth83
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A taxi service charges a base fare of $5, and a rate of $M per mile fo 31 Mar 2025, 21:52
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Difference: 3 + 8M Amount paid by A: 8(1 + M)
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55% (hard)

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72% (03:08) correct 28% (03:03) wrong based on 268 sessions

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A taxi service charges a base fare of $5, and a rate of $M per mile for the first 10 miles. Thereafter the rate is $0.5M per mile. There is also a charge of $3 per suitcase. Students traveling from and to the local college get a twenty percent discount on the mileage rates. A is a teacher traveling a distance of 8 miles with one suitcase. B is a student traveling 30 miles with two suitcases from the college to the station.

Select the expression for the difference between the amounts paid by A and B in dollars, and for the amount paid by A in dollars.
Difference Amount paid by A
8(1 + M)
3 + 8M
3 + 16M
11 + 16M
3(1 + 8M)
8M
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Difference: 3 + 8M Amount paid by A: 8(1 + M)
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A taxi service charges a base fare of $5, and a rate of $M per mile fo 31 Mar 2025, 22:29
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Shouldn't the difference be 2+8M?
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A taxi service charges a base fare of $5, and a rate of $M per mile fo 31 Mar 2025, 22:32
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A - Base Charge - 5$ , Suitcase Charge -3 $ and first 8 Miles - 8M $ :: A Total - 8 + 8M
B - Base Charge - 5$ , Suitcase Charge -3*2 = 6$ and first 10 Miles = 10M$ Remaining 20 Miles = 20*0.5M = 10M$ . Total for Mileage - 20$ . But for students 20% Discount on Mileage Rates - 0.8*20 = 16$ :: B Total = 11 + 16$

Therefore A Paid 8+8M = 8(1+M)
Difference = 11 + 16M - 8 - 8M = 8M + 3
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A taxi service charges a base fare of $5, and a rate of $M per mile fo 31 Mar 2025, 22:43
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Bismuth83
A taxi service charges a base fare of $5, and a rate of $M per mile for the first 10 miles. Thereafter the rate is $0.5M per mile. There is also a charge of $3 per suitcase. Students traveling from and to the local college get a twenty percent discount on the mileage rates. A is a teacher traveling a distance of 8 miles with one suitcase. B is a student traveling 30 miles with two suitcases from the college to the station.

Select the expression for the difference between the amounts paid by A and B in dollars, and for the amount paid by A in dollars.

Given rates

Base fare $5

For the first 10 miles $ M per mile

For every additional mile after first 10 miles = $0.5M per mile.

Per suitcase rate = $3

Teachers DONOT get discount in mileage rates

Students GET DISCOUNT IN MILEAGE RATES ONLY.

TEACHER travels for 8 miles with 1 suitcase.

Teacher rate = Base fare + mileage fare for 8 miles + per suitcase fare

= $5 + 8* $M + $3
= 8 + 8M
= 8 ( 1+ M)

Student travels for 30 miles with 2 suitcases in hand.

Student rate
= base fare + mileage rate for first 10 miles + mileage rate for the next 20 miles + 2* per suitcase rate .

= 5 + 10M + 20* 0.5 M + 2*3
= 11 + 20 M

They have given a discount of 20% on mileage rates only.

= 11 + 80/100 * 20 M

= 11 + 16 M

DIFFERENCE BETWEEN STUDENT RATE AND TEACHER RATE

= 11 + 16 M - ( 8 + 8M )

= 8M + 3
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A taxi service charges a base fare of $5, and a rate of $M per mile fo 31 Mar 2025, 22:51
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For given conditions
For A
Base fare=5
Fare for 8 km travel = 8xM = 8M
Suitcase charge = 3
Total = 8+8M = 8(1+M)

For B
Base fare = 5
Discount available for student = 20% = Factor of 0.8
Fare for first 10 km = 10xMx0.8
Fare for next 20 km = 20 x M x 0.8
Suitcase = 2 x 3 = 6
Total = 5 + 8M + 8M + 3 = 11 + 16M

Difference = 3 + 8M
For A = 8(1+M)
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A taxi service charges a base fare of $5, and a rate of $M per mile fo 01 Apr 2025, 01:27
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Bismuth83
A taxi service charges a base fare of $5, and a rate of $M per mile for the first 10 miles. Thereafter the rate is $0.5M per mile. There is also a charge of $3 per suitcase. Students traveling from and to the local college get a twenty percent discount on the mileage rates. A is a teacher traveling a distance of 8 miles with one suitcase. B is a student traveling 30 miles with two suitcases from the college to the station.

Select the expression for the difference between the amounts paid by A and B in dollars, and for the amount paid by A in dollars.
Solution:

Amount paid by A(teacher)

8 miles * M per mile + $5 + $3 = 8M + 8 = 8(M + 1)

Amount paid by B(student)

10 * 0.8M = 8M
10 * 0.4M = 4M
10 * 0.4M = 4M

Total = 16M + ($3*2) + 5 = 16M + 11


Difference between the Amount paid by A and B

(8M + 8) - ( 16M + 11) = 8M + 3

Amount paid by A = 8(M + 1)

Difference of Amount between A & B = 8M + 3
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A taxi service charges a base fare of $5, and a rate of $M per mile fo 01 Apr 2025, 11:20
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1. The question essentially asks us to find the cost of the ride A is going to take and the cost of the ride B is going to take.

2. Let's mark these values as \(S_A\) and \(S_B\), respectively, and calculate them.

3. \(S_A\).

- The base fare is $5.
- No discount is applied to the mileage rates since A is not a student.
- The total distance is 8 miles, which is no more than 10, so they'll be charged with a rate of $M. In other words, the cost from that will be $M\( * \)8 = 8M.
- One suitcase is equivalent to a fare of $3\( * \)1 = $3.

Finally, we can add up the costs and arrive at \(S_A = 5 + 8M + 3 = 8M + 8 = 8(M + 1)\).

4. \(S_B\).

- The base fare is $5.
- A discount is applied to the mileage rates since B is a student.
- The total distance is 30 miles, which is more than 10, so they'll be charged with a rate of $M for 10 miles and a rate of $0.5M for 20 miles. In other words, the cost from that will be $M\( * \)10 + $0.5M\( * \)20 = 10M + 10M = 20M and with a 20% discount, 20M\( * \)(100% - 20%) = 16M.
- Two suitcases are equivalent to a fare of $3\( * \)2 = $6.

Finally, we can add up the costs and arrive at \(S_B = 5 + 16M + 6 = 16M + 11\).

5. The positive difference between \(S_A\) and \(S_B\) is \(S_B - S_A = (16M + 11) - (8M + 8) = 8M + 3\).

6. Our answer will be: Difference - 3 + 8M and Amount paid by A - 8(1 + M).
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