Question

A manufacturer is preparing 3 shipments. each small crate in the shipment weighs the same, and each large crate in the shipment weighs the same. A worker records the contents of each shipment.
-shipment one contains 50 small crates and 32 large crates. The shipment weighs a total of 4170 pounds.
-shipment to contains 25 small crates and 40 large crates. The shipment weighs a total of 3525 pounds.
-shipment three 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 three?

Answer 1

The total weight of the shipment three in pounds is 2430 pounds

Each small crate in the shipment weighs the same and each large crate in the shipment weighs the same. Therefore,

Let

x = weight of each small crate

y = weight of each large crate

Therefore, for a shipment that contains 50 small crates and 32 large crates and weighs a total of 4170 pounds can be represented as follows:

• 50x + 32y = 4170

For a shipment that contains 25 small crates and 40 large crates and weighs a total of 3525 pounds can be represented as follows:

• 25x + 40y = 3525

Simultaneous Equation:

50x + 32y = 4170

25x + 40y = 3525

50x + 80y = 7050

50x + 32y = 4170

48y = 2880

y = 2880 / 48

y = 60

Therefore,

50x + 32(60) = 4170

50x = 2250

x = 2250 / 50

x = 45

The shipment three have the following weight:

• 30(45) + 18(60) = 1350 + 1080 = 2430 pounds

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