To confuseing I need help.
In honor of school spirit week, the student council decided to decorate lockers in the main lobby. The 9th graders officers stuck a decal of Smiley, the school mascot, on every third locker, starting with the third. The 10th graders officers taped a coupon for a free soda for the saturday game on every fourth locker, starting with the fourth. The junior class officers put black and purple ribbons, the school colors, on every 6th locker,starting with the sixth locker. Thesenior class officers usedwashable paint and painted the words "GO TEAM GO" on every 8th locker, beginning with the 8th locker.
-Which is the 1st locker to have all 4 items placed on it? Explain answer.
-If the hallway has a total of 1000 lockers, how many of those lockers will have all 4 items placed on it? explain.
-How many lockers will have only black and purple ribbons placed on it and no other items? explain.
the nineth graders
-992 lockers
-975 lockers
she is trust me
To find the first locker to have all four items placed on it, we need to determine the lowest common multiple (LCM) of the numbers 3, 4, 6, and 8.
1. Start by listing the multiples of each number and find the smallest multiple they have in common:
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
- Multiples of 6: 6, 12, 18, 24, 30, 36, ...
- Multiples of 8: 8, 16, 24, 32, 40, ...
From the lists, the smallest multiple that is common to all four numbers is 24.
2. Now, we need to determine which locker is the 1st locker to have all four items placed on it. We start counting the lockers from the first locker.
- Locker 1: No items.
- Locker 2: No items.
- Locker 3: Smiley decal (1st item placed).
- Locker 4: Free soda coupon (2nd item placed).
- Locker 5: No items.
- Locker 6: Black and purple ribbons (3rd item placed).
- Locker 7: No items.
- Locker 8: "GO TEAM GO" paint (4th item placed).
- Locker 9: Smiley decal (5th item, repeat of 1st item placed).
- Locker 10: Free soda coupon (6th item, repeat of 2nd item placed).
- Locker 11: No items.
- Locker 12: Black and purple ribbons (7th item, repeat of 3rd item placed).
- Locker 13: No items.
- Locker 14: No items.
- Locker 15: Smiley decal (8th item, repeat of 1st item placed).
- Locker 16: No items.
- Locker 17: No items.
- Locker 18: "GO TEAM GO" paint (9th item, repeat of 4th item placed).
- Locker 19: No items.
- Locker 20: Free soda coupon (10th item, repeat of 2nd item placed).
- Locker 21: No items.
- Locker 22: No items.
- Locker 23: Black and purple ribbons (11th item, repeat of 3rd item placed).
- Locker 24: Smiley decal, free soda coupon, black and purple ribbons, "GO TEAM GO" paint (all four items placed).
Therefore, the 1st locker to have all four items placed on it is Locker 24.
To find the number of lockers that will have all four items placed on them out of a total of 1000 lockers, we divide 1000 by the LCM of 3, 4, 6, and 8 (which we found to be 24).
The number of lockers = 1000 ÷ 24 = 41 remainder 16.
There will be 41 lockers with all four items placed on them out of the total 1000 lockers.
To calculate the number of lockers with only black and purple ribbons placed on them (and no other items), we need to determine the number of multiples of 6 (which represents the lockers with the ribbons).
1. Divide 1000 by 6 (as it is the least common multiple of 3, 4, 6, and 8) to find the number of sets of 6 lockers in the hallway: 1000 ÷ 6 = 166 remainder 4.
2. Since the remainder is 4, it means there will be an additional 4 lockers beyond the complete sets of 6.
Therefore, there will be 166 sets of 6 lockers (996 lockers) and an additional 4 lockers with only black and purple ribbons placed on them, and no other items.
In this case, a total of 4 lockers will have only black and purple ribbons placed on them, and no other items.