SOLUTION: Mrs. Flanagan manages a hotel. One day, she received a certain number of cancellations. Then she received reservations that were 13 more than 4 times the number of cancellations.

Algebra ->  Inverses -> SOLUTION: Mrs. Flanagan manages a hotel. One day, she received a certain number of cancellations. Then she received reservations that were 13 more than 4 times the number of cancellations.      Log On


   

Question 1104046: Mrs. Flanagan manages a hotel. One day, she received a certain number of
cancellations. Then she received reservations that were 13 more than 4 times the
number of cancellations. There were 79 hotel reservations in all.
How many cancellations did Mrs. Flanagan receive?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
net reservations = reservations - cancellations.

let n represent net number of reservations.
let r represent number of reservations.
let c represents number of cancellations.

formula becomes n = r - c

you are given that net number of reservations are 79.

these would be reservations that haven't been cancelled.

formula of n = r - c becomes 79 = r - c.

you are given that number of reservations are 13 more than 4 times cancellations.

formula for that would be r = 4 * c + 13.

since r = 4 * c + 13, replace r with 4 * c + 13 in formula of 79 = r - c to get 79 = 4 * c + 13 - c

combine like terms to get 79 = 3 * c + 13.

subtract 13 from both sides of this equation to get 66 = 3 * c.

solve for c to get c = 22.

go back to the equation of 79 = r - c.

when c = 22, this equation becomes 79 = r - 22.

add 22 to both sides of this equation to get 101 = r

there were 101 reservations made.
there were 22 cancellations.
the net reservations were 104 - 22 = 79.

since you were only asked to find the number of cancellations, then your solution is 22.