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, 𝑥, 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 𝑥, where 𝑥 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 𝑥.
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 40𝑥 must
be less than or equal to 1000 plus 100𝑥. We can subtract 40𝑥 from both
sides of the inequality. Subtracting 40𝑥 from the left-hand
side leaves us with 1300. And subtracting 40𝑥 from 100𝑥
gives us 60𝑥. 1300 is less than or equal to 1000
plus 60𝑥. 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 60𝑥.
Finally, we can divide both sides
by 60. 300 divided by 60 is equal to
five. And 60𝑥 divided by 60 equals a
𝑥. Therefore, five is less than or
equal to 𝑥. We can rewrite this inequality so
that the 𝑥 is on the left-hand side. 𝑥 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.
