A taxi service charges a base fare of $5, and a rate of $M per mile fo

Question

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.

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.

Mallikaarora · Answer

Shouldn't the difference be 2+8M?

Magician25 · Answer

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

Dereno · Answer

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

rohitz98 · Answer

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)

GmatTest2026 · Answer

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

Bismuth83 · Answer

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)  .

bumpbot · Answer

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A taxi service charges a base fare of $5, and a rate of $M per mile fo

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Difference	Amount paid by A
		8(1 + M)
		3 + 8M
		3 + 16M
		11 + 16M
		3(1 + 8M)
		8M

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