High School

The time has come! The ship is stocked with supplies and equipment, the crew have said their goodbyes, and the way through the myriad governmental and international rigor has been paved. The journey begins and all involved have treasure in their eyes. (1) The crew prefers an orange juice that is approximately 12% orange concentrate. How much pure orange concentrate and how much water will the steward use to make a total of 600 gallons of the preferred juice? (2) During the voyage, the crew will receive a total of 28100 communication transmissions in the form of email, cellphone calls/texts, and calls over the ship's satellite telephone. There is an expectation that the cellphone calls/texts will outnumber the combination of email and sat-phone transmissions by 1100 . If the average number of minutes spent fielding each email, cell call/text, and sat call is 8,3 , and 5 , respectively, and the total average number of minutes spent on all transmissions is 136200 , how many transmissions of each type will be made during the voyage? (3) To facilitate stops at ports-of-call and to safely navigate international waters, three primary governments will require significant payments. The agreements restrict the number of minutes the ship can spend in the ports of their countries to 0.0008,0.0012, and 0.0003 minutes for every dollar paid, and the security and deployment cost for every naval escort ship provided is $250000,$200000, and $500000, respectively. If there will be a total of 3150 minutes for stops in ports, a total of 16 escort ships provided, and a total bill of $5000000, how much money will each government require?

Answer :

The steward will use 72 gallons of pure orange concentrate and 528 gallons of water to make a total of 600 gallons of the preferred juice.

How to calculate the value

The concentration of orange concentrate is 12%, which means that 12% of the total volume will be pure orange concentrate. This can be expressed as:

x = 0.12 * 600

Simplifying, we have:

x = 72

Since the total volume of the juice is 600 gallons, the amount of water can be calculated as:

y = 600 - x

= 600 - 72

= 528

Therefore, the steward will use 72 gallons of pure orange concentrate and 528 gallons of water to make a total of 600 gallons of the preferred juice.

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