A logistics company operates two types of delivery trucks: Model A and Model B. Model A co… — GMAT

A logistics company operates two types of delivery trucks: Model A and Model B. Model A consumes $0.25$ liters of fuel per mile and incurs $\$1.50$ in maintenance costs per mile. Model B consumes $0.40$ liters of fuel per mile and incurs $\$1.00$ in maintenance costs per mile. On a given day, the fleet consumed a total of $300$ liters of fuel and incurred a total of $\$1,100$ in maintenance costs. What was the total number of miles traveled by the Model A trucks on that day?

Answer: 400 miles

Answer

The Model A trucks traveled a total of 400 miles on that day.

Let

x

be the number of miles driven by Model A trucks and

y

be the number of miles driven by Model B trucks. Set up two equations:

0.25x + 0.40y = 300

(fuel) and

1.50x + 1.00y = 1100

(maintenance). Substituting

y = 1100 - 1.5x

into the fuel equation yields

0.25x + 0.40(1100 - 1.5x) = 300

, which simplifies to

-0.35x + 440 = 300

, leading directly to

x = 400

Step-by-Step Solution

Formulate the linear system

0.25x + 0.40y = 300

and

1.50x + 1.00y = 1100

, where

x

is miles driven by Model A and

y

is miles driven by Model B.

Translates the rates of fuel consumption and maintenance per mile into total daily figures.

Express

y

in terms of

x

y = 1100 - 1.5x

Isolating

y

makes substitution into the fuel equation straightforward.

Substitute

y

into the first equation and solve for

x

0.25x + 0.40(1100 - 1.5x) = 300 \implies -0.35x + 440 = 300 \implies -0.35x = -140 \implies x = 400

Reduces the system to a single linear equation in

x

to find the distance for Model A.

Key Concept

Setting up and solving a two-variable system of linear equations via substitution or elimination.

Question

Answer

Step-by-Step Solution

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