Examkin

Question

Difficulty: HardUS Customary Capacity and Volume

A coffee shop prepares cold brew coffee in large batches. Each batch produces exactly 33 gallons and 22 quarts of cold brew. The shop needs to completely fill three 44-gallon dispensers and two 22-gallon dispensers. If the shop has already prepared 704704 fluid ounces of cold brew, how many additional full batches must they prepare today to have enough cold brew to exactly fill all the dispensers?

Answer: 3 batches

Answer

3 batches
The correct answer is found by establishing a common unit of measurement, such as quarts. The total dispenser capacity is 16 gallons, which equals 64 quarts. The existing 704 fluid ounces is converted to 22 quarts (since there are 32 fluid ounces in a quart). Subtracting the 22 existing quarts from the 64 required quarts leaves 42 quarts needed. Finally, since one batch produces exactly 14 quarts (3 gallons + 2 quarts), we divide the 42 quarts needed by 14 quarts per batch to determine that 3 batches are required.

Step-by-Step Solution

1
Calculate the total required volume in gallons.
16 gallons
To find out the total capacity of the three 4-gallon dispensers and two 2-gallon dispensers.
2
Convert the total required volume from gallons to quarts.
64 quarts
Using a smaller common unit (quarts) makes it easier to subtract the existing fluid ounces and divide by the batch size.
3
Convert the already prepared cold brew from fluid ounces to quarts.
22 quarts
There are 32 fluid ounces in 1 quart. Dividing 704 by 32 gives the amount in quarts so it can be subtracted from the total.
4
Determine the remaining volume of cold brew needed.
42 quarts
Subtracting the existing volume (22 quarts) from the total required volume (64 quarts) gives the amount that still needs to be prepared.
5
Convert the volume of one batch to quarts.
14 quarts
One batch is 3 gallons (12 quarts) plus 2 quarts, which equals 14 quarts. This gives the unit rate per batch.
6
Calculate the number of additional batches needed.
3
Dividing the remaining needed volume (42 quarts) by the volume per batch (14 quarts) yields the exact number of batches required.

Key Concept

Converting and performing multi-step operations with US Customary units of capacity (gallons, quarts, and fluid ounces).
Estimated Time:2m 30s
Rate this question

Topics

US Customary Capacity and Volume

More questions from this topic