David and Robert each bought a meal at a restaurant. The price of David’s meal was 𝑥 dollars, and the price of Robert’s meal was 5 dollars more than the price of David’s meal. If David and Robert split the cost of the meals evenly and paid a 10 percent tip each, which of the following expressions represents the amount, in dollars, that each of them paid? Assume there is no sales tax. Is it option A) 0.1𝑥 plus 0.1, option B) 2.2𝑥 plus 5.5, option C) 0.1𝑥 plus 5.5, or option D) 1.1𝑥 plus 2.75?
We’re told in the question that the price of David’s meal was 𝑥 dollars. Robert’s meal was 5 dollars more. Therefore, an expression for Robert’s meal is 𝑥 plus five. We can calculate the total cost of the meals before the tip by adding 𝑥 and 𝑥 plus five. 𝑥 plus 𝑥 is equal to two 𝑥. Therefore, the total cost of the two meals is two 𝑥 plus five.
We’re told that David and Robert paid a 10 percent tip. 10 percent is equivalent to 0.1. Therefore, the tip was equal to 0.1, multiplied by two 𝑥 plus five. Distributing the parentheses here gives us 0.2𝑥 plus 0.5, as 0.1 multiplied by two is 0.2, and 0.1 multiplied by five is 0.5. The total amount that David and Robert therefore paid, including the tip, is two 𝑥 plus five plus 0.2𝑥 plus 0.5. Once again, we can collect the like terms. Two 𝑥 plus 0.2𝑥 is equal to 2.2𝑥. And five plus 0.5 is equal to 5.5.
The final part of the question is to calculate how much they paid each. And we’re told that they split the bill evenly. This means that we need to divide 2.2𝑥 plus 5.5 by two. 2.2𝑥 divided by two is equal to 1.1𝑥, as a half of 2.2 is 1.1. 5.5 divided by two is equal to 2.75, as a half of five is 2.5, and a half of 0.5 is 0.25. Adding these together gives us 2.75. The correct expression for the amount of money in dollars that David and Robert paid each is 1.1𝑥 plus 2.75. This means that the correct answer was option D.