SOLUTION: Fiona wants to buy a new house but she doesn't want a house with the numbers that are divisable by 3 or 5. If all the houses numbered between 100 and 150 inclusive are for sale how

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: Fiona wants to buy a new house but she doesn't want a house with the numbers that are divisable by 3 or 5. If all the houses numbered between 100 and 150 inclusive are for sale how      Log On


   



Question 265049: Fiona wants to buy a new house but she doesn't want a house with the numbers that are divisable by 3 or 5. If all the houses numbered between 100 and 150 inclusive are for sale how many houses can she choose from?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The multiples of 3 that are included in
houses numbered 100-150 are:
34 x 3 = 102
35 x 3 = 105
36 x 3 = 108
up to:
50 x 3 = 150
And the multiples of 5 are:
20 x 5 = 100
21 x 5 = 105
22 x 5 = 110
up to
30 x 5 = 150
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I don't want to count house numbers twice, so
in the 1st list I'll pull out thoses divisible by 5
35 x 3
40 x 3
45 x 3
50 x 3
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The 1st list has 50+-+34+%2B+1+=+17 entries
I want to delete 4
17+-+4+=+13
The 2nd list has 30+-+20+%2B+1+=+11 entries
13+%2B+11+=+24
There are 24 house numbers she doesn't want
150+-+100+%2B+1+=+51 possible numbers
51+-+24+=+27
She can choose from 27 houses
Hope I got it right!