Question

use the information to answer the question.
a manufacturer is preparing 3 shipments. each small crate in the shipment weighs the same, and each large crate in the shipment weighs
a worker records the contents of each shipment.

• shipment 1 contains 50 small crates and 32 large crates. the shipment weighs a total of 4170 pounds.
• shipment 2 contains 25 small crates and 40 large crates. the shipment weighs a total of 3525 pounds.
• shipment 3 contains 30 small crates and 18 large crates. the worker did not record the total weight of the shipment.

what is the total weight, in pounds, of shipment 3? enter the answer in the box.
pounds

Explanation:

Step1: Define variables

Let \( s \) be the weight of a small crate (in pounds) and \( l \) be the weight of a large crate (in pounds).
From Shipment 1: \( 50s + 32l = 4170 \)
From Shipment 2: \( 25s + 40l = 3525 \)

Step2: Simplify Shipment 2 equation

Multiply the second equation by 2: \( 50s + 80l = 7050 \)

Step3: Subtract Shipment 1 equation

Subtract the first equation (\( 50s + 32l = 4170 \)) from the new second equation:
\( (50s + 80l) - (50s + 32l) = 7050 - 4170 \)
\( 48l = 2880 \)
\( l = \frac{2880}{48} = 60 \)

Step4: Find \( s \) using Shipment 2 equation

Substitute \( l = 60 \) into \( 25s + 40l = 3525 \):
\( 25s + 40(60) = 3525 \)
\( 25s + 2400 = 3525 \)
\( 25s = 3525 - 2400 = 1125 \)
\( s = \frac{1125}{25} = 45 \)

Step5: Calculate Shipment 3 weight

Shipment 3 has 30 small crates and 18 large crates.
Weight = \( 30s + 18l \)
Substitute \( s = 45 \) and \( l = 60 \):
\( 30(45) + 18(60) = 1350 + 1080 = 2430 \)

Answer:

2430