An urban courier service dispatches two types of electric cargo bikes, Cargo-X and Cargo-Y… — GMAT

An urban courier service dispatches two types of electric cargo bikes, Cargo-X and Cargo-Y, for package deliveries. On Monday, a fleet of 3 Cargo-X bikes and 4 Cargo-Y bikes completed a total of 38 package deliveries. On Tuesday, a fleet of 5 Cargo-X bikes and 2 Cargo-Y bikes completed a total of 40 package deliveries. Assuming each bike of a given type completes a constant number of deliveries per day, how many total package deliveries will a combined fleet of 4 Cargo-X bikes and 3 Cargo-Y bikes complete in one day?

Answer: 39 deliveries

Answer

A combined fleet of 4 Cargo-X bikes and 3 Cargo-Y bikes will complete 39 package deliveries in one day.

Solving the linear system

3x + 4y = 38

and

5x + 2y = 40

gives

x = 6

deliveries per Cargo-X bike and

y = 5

deliveries per Cargo-Y bike. Substituting these rates into

4x + 3y

yields

4(6) + 3(5) = 39

total deliveries.

Step-by-Step Solution

Formulate a system of linear equations representing the delivery totals.

System established:

3x + 4y = 38

and

5x + 2y = 40

, where

x

and

y

represent the daily delivery capacities of Cargo-X and Cargo-Y bikes.

Translates contextual problem statements into quantitative algebraic equations.

Solve the system using elimination or substitution.

x = 6

deliveries per Cargo-X bike and

y = 5

deliveries per Cargo-Y bike.

Determines the exact rate per vehicle type.

Evaluate the target linear combination

4x + 3y

4(6) + 3(5) = 39

Computes the total capacity for the requested fleet combination.

Key Concept

Solving systems of simultaneous linear equations in two variables

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