There were 360 pumpkins in a pumpkin patch, but it was difficult for Farmer Joe to Find the perfect pumpkin.
Every 3rd pumpkin was too small
Every 4th pumpkin was too green
Every 5th pumpkin had a broken steam
Every 6th pumpkin had the wrong shape.
How many perfect pumpkins did Farmer Joe find in the pumpkin patch?
Can you please show a complete explanation of your work.
Than You Really Appreciate It?
2007-10-30 12:17:11 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Every 3rd:
360 / 3 = 120 perfect pumpkins
Every 4th:
360 / 4 = 90 perfect pumpkins
Every 5th:
360 / 5 = 72 perfect pumpkins
Every 6th:
360 / 6 = 60 perfect pumpkins
2007-10-30 12:51:30 · answer #1 · answered by Nizam89 3 · 0⤊ 0⤋
If you take the numbers between 1 and 360 and remove those that have at least any one of the factors 3 through 6 , the remainder will be perfect. Remember, that some pumpkins can have multiple defects, so you can't do this in steps.
For factor 3, there are 120 defective pumpkins. However, 1 of four of these also include defect 4.
1 of five include defect 5 and 1 of 6 include defect 6. Call these by their defects, we have
3/4=30, 3/5=24 and 3/6=20.
Now factor 4 pumpkins total 90, but we have already excluded 30 above. In a like manner, 4/5=18 and 4/6=15. So we have really excluded 60 more
Factor 5 pumpkins total 72, but we have excluded
42 of these already, so we have added 30. We also exclude by union (5/6) 12 more pumpkins.
Factor 6 pumplins total 60, but we have excluded 47 already, leaving 13 additional pumpkins excluded.
The total exclusions are 120+60+30+13? = 223 leaving 137 perfect pumpkins.
2007-10-30 19:37:39 · answer #2 · answered by cattbarf 7 · 0⤊ 1⤋
hmmm.. i didnt have time to do this, but i think its ....about 120 perfect pumkins
2007-10-30 19:27:22 · answer #3 · answered by iHeartChem 2 · 0⤊ 1⤋
well the answer is all the prime numbers, but im not doing that,
2007-10-30 19:25:42 · answer #4 · answered by lil b 2 · 0⤊ 1⤋