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30 Mar 2024, 12:36
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According to the new estimates, the number of stars in the Milky Way galaxy has increased from 124 billion to 415 billion, while the number of stars in the Andromeda galaxy has doubled. With these updated figures, the number of stars in the Milky Way is still only 42% of the number of stars in the Andromeda galaxy. Prior to the new estimates, approximately how many times more stars did the Andromeda galaxy have compared to the Milky Way galaxy?
A. 2
B. 4
C. 5
D. 8
E. 16
A. 2
B. 4
C. 5
D. 8
E. 16
30 Mar 2024, 12:36
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Official Solution:
According to the new estimates, the number of stars in the Milky Way galaxy has increased from 124 billion to 415 billion, while the number of stars in the Andromeda galaxy has doubled. With these updated figures, the number of stars in the Milky Way is still only 42% of the number of stars in the Andromeda galaxy. Prior to the new estimates, approximately how many times more stars did the Andromeda galaxy have compared to the Milky Way galaxy?
A. 2
B. 4
C. 5
D. 8
E. 16
We are tasked with approximating, so let's proceed with that approach.
Consider using 400 billion instead of 415 billion, and 40% instead of 42%. This gives us: 400 billion = 0.4*(Andromeda's new estimate). Notice that the first approximation decreases the new estimate for the Andromeda galaxy, while the second approximation increases it. Therefore, these two approximations roughly balance each other out. Thus, from 400 billion = 0.4*(Andromeda's new estimate), we determine that Andromeda's new estimate is 1,000 billion. Given that the new estimates have doubled the numbers for the Andromeda galaxy, its old number was 500 billion.
Consequently, prior to the new estimates, the Andromeda galaxy had \(\frac{500}{124} \approx 4\) times more stars than the Milky Way galaxy.
Answer: B
According to the new estimates, the number of stars in the Milky Way galaxy has increased from 124 billion to 415 billion, while the number of stars in the Andromeda galaxy has doubled. With these updated figures, the number of stars in the Milky Way is still only 42% of the number of stars in the Andromeda galaxy. Prior to the new estimates, approximately how many times more stars did the Andromeda galaxy have compared to the Milky Way galaxy?
A. 2
B. 4
C. 5
D. 8
E. 16
We are tasked with approximating, so let's proceed with that approach.
Consider using 400 billion instead of 415 billion, and 40% instead of 42%. This gives us: 400 billion = 0.4*(Andromeda's new estimate). Notice that the first approximation decreases the new estimate for the Andromeda galaxy, while the second approximation increases it. Therefore, these two approximations roughly balance each other out. Thus, from 400 billion = 0.4*(Andromeda's new estimate), we determine that Andromeda's new estimate is 1,000 billion. Given that the new estimates have doubled the numbers for the Andromeda galaxy, its old number was 500 billion.
Consequently, prior to the new estimates, the Andromeda galaxy had \(\frac{500}{124} \approx 4\) times more stars than the Milky Way galaxy.
Answer: B
17 Jul 2025, 11:30
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415=0,42*2X
X=415/0,84 ...if 415/1 is 415...415/0,84 would be more than that, and close to 500...
So, compared with 124... 2 times is too low, 5 times is too high....124 x 4 ≈ 500
Answer B= 4
X=415/0,84 ...if 415/1 is 415...415/0,84 would be more than that, and close to 500...
So, compared with 124... 2 times is too low, 5 times is too high....124 x 4 ≈ 500
Answer B= 4
