Math Problems -

Question

1. The sum of the first and third of three consecutive odd integers is 214 Find the consecutive integers
2. Including 8% sales tax, an inn charges $172.80 per night. Find the nightly cost at the inn before tax is added. (a) Write an equation to model the problem. Let  represent the nightly cost before tax. (b) Solve the equation to find nightly cost before tax.
3. Consider the following process. Take a positive integer n. A new number is created by taking the sum of the squares of its digits. Repeat. If this process ever reaches the number 1, then n is called a "happy" number. For example, if n = 34, then after iterating this process once we get  Let n = 4. Give the first three numbers created by following this process. Number after 1 iteration:  .Number after 2 iterations:  .Number after 3 iterations:  .
4.  you have a playlist with 12 pop songs and 13 R&B songs. You randomize and hit play.

How many songs do you have to listen to in order to guarantee you hear two songs from the same genre?   .

How many songs do you have to listen to in order to guarantee you hear two R&B songs?   .

How many songs do you have to listen to in order to guarantee you hear one R&B song and one pop song?  .

Answer 1

F+T =214

x+x+4 = 214

2x = 210

x = 210/2 = 105

the numbers are 105,107, and 109