A logistics company dispatches a fleet of delivery vehicles consisting entirely of Van A m… — GMAT

A logistics company dispatches a fleet of delivery vehicles consisting entirely of Van A models and Van B models for a day's operations. Each Van A carries $40$ packages and consumes $5$ gallons of fuel per route. Each Van B carries $60$ packages and consumes $8$ gallons of fuel per route. On a given day, $18$ vans were dispatched in total, delivering a combined total of $920$ packages. Which of the following statements must be true? Select all that apply.

The total number of Van B models dispatched was $10$ .Cevap
B
The total fuel consumed by all Van A models combined was $50$ gallons.
Van B models accounted for more than $60\%$ of the total fuel consumed by the fleet.Cevap
D
The ratio of the number of Van A models to Van B models dispatched was $5$ to $4$ .
The total fuel consumed by the entire fleet was $120$ gallons.Cevap

Cevap

The true statements are those stating that 10 Van B models were dispatched, that Van B models accounted for more than 60% of total fleet fuel consumed, and that the total fuel consumed by the entire fleet was 120 gallons.

Solving the linear system

A + B = 18

and

40A + 60B = 920

yields

A = 8

Van A models and

B = 10

Van B models. Evaluating the claims: 10 Van B models were dispatched (true); Van B fuel (

80

gallons) represents

80/120 = 66.67\%

of total fuel, which is greater than

60\%

(true); and total fleet fuel consumption is

40 + 80 = 120

gallons (true).

Adım Adım Çözüm

Define variables and construct the system of linear equations.

Let

A

be the number of Van A models and

B

be the number of Van B models. Total vans equation:

A + B = 18

. Total packages equation:

40A + 60B = 920

Word problem modeling requires translating fleet count and package delivery totals into algebraic linear equations.

Solve the system of equations for

A

and

B

Divide the package equation by

20

2A + 3B = 46

. Substitute

A = 18 - B

2(18 - B) + 3B = 46 \implies 36 + B = 46 \implies B = 10

. Then

A = 18 - 10 = 8

Determining exact vehicle quantities is required to evaluate all downstream statements.

Calculate total fuel consumption for each van model and the entire fleet.

Van A fuel:

8 \text{ vans} \times 5 \text{ gal/van} = 40 \text{ gallons}

. Van B fuel:

10 \text{ vans} \times 8 \text{ gal/van} = 80 \text{ gallons}

. Total fleet fuel:

40 + 80 = 120 \text{ gallons}

Provides exact quantities to test statement validity.

Evaluate each statement against the calculated values.

1) Van B count is 10 (True). 2) Van A fuel is 40 gallons, not 50 (False). 3) Van B fuel percentage is

80/120 = 66.67\% > 60\%

(True). 4) Van A to Van B ratio is

8:10 = 4:5

, not

5:4

(False). 5) Total fuel is 120 gallons (True).

Identifies all correct options for multiple selection.

Anahtar Kavram

Linear Equation System Modeling in Applied Contexts

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