A reservation clerk worked 15.3 hours one day. She spent twice as much time entering new reservations as she did verifying old ones and one and a half as much time calling to confirm reservations as verifying old ones. How much time did she spend entering new reservations?
What formula would I use to solve this problem?
Well, it seems like the reservation clerk had quite the eventful day! To figure out how much time she spent entering new reservations, let's use a formula that would make any math enthusiast chuckle: the "Laughingly Simple Equation"!
Let's say the time spent verifying old reservations is represented by V, and the time spent calling to confirm reservations is represented by C. Now, since the clerk spent twice as much time entering new reservations as verifying old ones, we can represent the time spent entering new reservations as 2V. Also, the time spent calling to confirm reservations was one and a half times the time spent verifying old ones, so C can be represented as 1.5V.
Now, if we add up the time spent on all three tasks, we get the total number of hours: V + 2V + 1.5V = 15.3
To solve this equation, we simply need to find the value of V, which represents the time spent verifying old reservations.
So, the formula you can use here is:
V + 2V + 1.5V = 15.3
Keep in mind that this equation is intended to bring a smile to your face, rather than being a conventional mathematical formula!
To solve this problem, we can represent the time spent entering new reservations as "x" hours. We are given that the time spent verifying old reservations is half of the time spent entering new reservations, so it would be "0.5x" hours. Additionally, the time spent calling to confirm reservations is one and a half times the time spent verifying old reservations, so it would be "1.5 * 0.5x" hours.
Therefore, the total time worked by the reservation clerk can be represented as:
x + 0.5x + 1.5 * 0.5x = 15.3 hours
To solve this equation, we need to simplify and find the value of "x".
To solve this problem, you can use a system of equations. Let's assume that the time spent verifying old reservations is x.
Given:
The time spent entering new reservations is twice as much as verifying old reservations, so it would be 2x.
The time spent calling to confirm reservations is one and a half as much as verifying old reservations, so it would be 1.5x.
Now, you have the equation:
x + 2x + 1.5x = 15.3
To solve this equation, combine like terms on the left side:
4.5x = 15.3
Then isolate x by dividing both sides by 4.5:
x = 15.3 / 4.5
Finally, calculate the value of x:
x = 3.4
Therefore, she spent 3.4 hours entering new reservations.