Video: US-SAT04S4-Q16-712176404837

Kevin is planning his summer vacation. He is interested in visiting one of the following cities: Singapore, Istanbul, or Bali. He gathered information from the Internet to help him decide the budget needed for his vacation. The given table shows the flight ticket prices for each of the three cities as well as the daily expenses needed for food and accommodation. Kevin can estimate the budget, 𝑦, in dollars. For what number of days, π‘₯, will the total budget for traveling to Bali be less or equal to the budget for traveling to Singapore?

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Video Transcript

Kevin is planning his summer vacation. He is interested in visiting one of the following cities: Singapore, Istanbul, or Bali. He gathered information from the Internet to help him decide the budget needed for his vacation. The given table shows the flight ticket prices for each of the three cities as well as the daily expenses needed for food and accommodation. Kevin can estimate the budget, 𝑦, in dollars. For what number of days, π‘₯, will the total budget for traveling to Bali be less or equal to the budget for traveling to Singapore?

Let’s firstly consider the cost of traveling to Singapore. The cost of the flight ticket is 1000 dollars. The daily expenses are 25 dollars for foods and 75 dollars for accommodation. This is a total of 100 dollars. The total budget required for Singapore would, therefore, be 1000 plus 100 multiplied by π‘₯, where π‘₯ is the number of days. The flight cost to Bali is 1300 dollars. Daily expenses are 15 dollars for food and 25 dollars for accommodation. 15 plus 25 is equal to 40. This means that the total budget required for Bali is 1300 plus 40 multiplied by π‘₯.

In this question, we want the budget for Bali to be less than or equal to the budget for Singapore. This means that 1300 plus 40π‘₯ must be less than or equal to 1000 plus 100π‘₯. We can subtract 40π‘₯ from both sides of the inequality. Subtracting 40π‘₯ from the left-hand side leaves us with 1300. And subtracting 40π‘₯ from 100π‘₯ gives us 60π‘₯. 1300 is less than or equal to 1000 plus 60π‘₯. We can now subtract 1000 from both sides of the new inequality. 1300 minus 1000 is equal to 300. Therefore, 300 is less than or equal to equal to 60π‘₯.

Finally, we can divide both sides by 60. 300 divided by 60 is equal to five. And 60π‘₯ divided by 60 equals a π‘₯. Therefore, five is less than or equal to π‘₯. We can rewrite this inequality so that the π‘₯ is on the left-hand side. π‘₯ is greater than or equal to five. This means that if Kevin travels to Bali for five or more days, then his budget will be last than or equal to the budget for traveling to Singapore. Bali becomes cheaper than Singapore after five days. If he was traveling for exactly five days, then the cost of both cities would be equal.

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