A logistics team is packing a shipment containing standard crates and heavy crates. A load… — Armed Services Vocational Aptitude Battery (ASVAB)

A logistics team is packing a shipment containing standard crates and heavy crates. A load of $4$ standard crates and $3$ heavy crates weighs a total of $170$ pounds. Another load consisting of $2$ standard crates and $5$ heavy crates weighs a total of $190$ pounds. Based on this information, what is the weight, in pounds, of a single heavy crate?

Answer: 30 pounds

Answer

The correct answer is found by translating the word problem into the system of equations

4x + 3y = 170

and

2x + 5y = 190

. By multiplying the second equation by

-2

, the

x

terms are eliminated when the equations are added, yielding

-7y = -210

, which simplifies to

y = 30

Step-by-Step Solution

Define variables for the unknown quantities.

Let

x

be the weight of a standard crate and

y

be the weight of a heavy crate.

To translate the word problem into a mathematical system of equations.

Set up a system of linear equations based on the given information.

Equation 1:

4x + 3y = 170

Equation 2:

2x + 5y = 190

To mathematically represent the total weights of the two different loads.

Use the elimination method to cancel out the

x

variable. Multiply Equation 2 by

-2

-2(2x + 5y) = -2(190) \Rightarrow -4x - 10y = -380

Creating a

-4x

term allows the

x

variables to be eliminated when added to the

4x

in Equation 1.

Add the new Equation 2 to Equation 1.

(4x + 3y) + (-4x - 10y) = 170 - 380 \Rightarrow -7y = -210

This leaves a single-variable equation that can be directly solved.

Solve for

y

y = \frac{-210}{-7} = 30

To isolate

y

, which represents the target value: the weight of the heavy crate.

Key Concept

Solving Systems of Linear Equations

Question

Answer

Step-by-Step Solution

Key Concept

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