Question

filling in a table
last july, 160 babies were born in a hospital in maine; \\(\frac{3}{5}\\) of the babies were girls. seventy babies weighed 8 pounds or more. fifty boys weighed 8 pounds or more.
\\(\circ\\) \\(a = 64, b = 14, c = 76, d = 20, e = 90\\)
\\(\circ\\) \\(a = 14, b = 64, c = 90, d = 20, e = 76\\)
\\(\circ\\) \\(a = 14, b = 76, c = 64, d = 90, e = 20\\)
\\(\circ\\) \\(a = 14, b = 64, c = 76, d = 20, e = 90\\)

Explanation:

Step1: Find total girls

Total babies = 160, fraction of girls = $\frac{3}{5}$, so girls = $\frac{3}{5}×160 = 96$. So girls' total (given as 96) matches. Total boys = 160 - 96 = 64. So boys' total \( b = 64 \).

Step2: Find girls with ≥8 lbs

Total ≥8 lbs = 70, boys with ≥8 lbs = 50, so girls with ≥8 lbs \( d = 70 - 50 = 20 \).

Step3: Find boys with <8 lbs

Boys' total \( b = 64 \), boys with ≥8 lbs = 50, so \( a = 64 - 50 = 14 \).

Step4: Find total <8 lbs

Total babies = 160, total ≥8 lbs = 70, so total <8 lbs \( e = 160 - 70 = 90 \)? Wait, no: Wait, total <8 lbs + total ≥8 lbs = 160. So total <8 lbs \( e = 160 - 70 = 90 \)? Wait, no, wait: girls' <8 lbs \( c = \) total girls - girls ≥8 lbs = 96 - 20 = 76. Then total <8 lbs \( e = a + c = 14 + 76 = 90 \)? Wait, no, let's check the options. Wait the options: Let's re-express.

Wait, let's list the table:

Rows: Boys, Girls, Total

Columns: <8 lbs, ≥8 lbs, Total

Boys: <8 lbs = a, ≥8 lbs = 50, Total = b

Girls: <8 lbs = c, ≥8 lbs = d, Total = 96

Total: <8 lbs = e, ≥8 lbs = 70, Total = 160

So:

1. Boys' total (b) = total babies - girls' total = 160 - 96 = 64. So b = 64.

2. Girls' ≥8 lbs (d) = total ≥8 lbs - boys' ≥8 lbs = 70 - 50 = 20. So d = 20.

3. Boys' <8 lbs (a) = boys' total - boys' ≥8 lbs = 64 - 50 = 14. So a = 14.

4. Girls' <8 lbs (c) = girls' total - girls' ≥8 lbs = 96 - 20 = 76. So c = 76.

5. Total <8 lbs (e) = total babies - total ≥8 lbs = 160 - 70 = 90. Wait, but e is also a + c = 14 + 76 = 90. So e = 90.

Now check the options:

Option 2: a=14, b=64, c=76, d=20, e=90? Wait no, the options given:

Wait the options are:

1. a=64, b=14, c=76, d=20, e=90 → no, b should be 64.

2. a=14, b=64, c=76, d=20, e=90? Wait the second option is "a=14, b=64, c=90 d=20, e=76" → no, c should be 76. Wait the third option? Wait the options as given:

Wait the user's options:

- a=64, b=14, c=76, d=20, e=90

- a=14, b=64, c=90 d=20, e=76

- a=14, b=76, c=64, d=90, e=20

- a=14, b=64, c=76, d=20, e=90 → Wait, maybe a typo in the options. Wait the second option: "a=14, b=64, c=90 d=20, e=76" → no. Wait the fourth option? Wait the user's options:

Wait the user wrote:

○ a=64, b=14, c=76, d=20, e=90

○ a=14, b=64, c=90 d=20, e=76

○ a=14, b=76, c=64, d=90, e=20

○ a=14, b=64, c=76, d=20, e=90 → Wait, maybe the second option has a typo, but the fourth option (if exists) or the second? Wait no, let's recheck.

Wait, according to our calculation:

a=14, b=64, c=76 (girls' <8 lbs: 96 - 20 =76), d=20, e=90 (total <8 lbs: 160 -70=90). So looking at the options, the second option is "a=14, b=64, c=90 d=20, e=76" → no, c should be 76, e should be 90. Wait the fourth option (if the user missed a circle) but the options given: Wait the user's options:

Wait the options are:

1. a=64, b=14, c=76, d=20, e=90 → no (b=14 wrong)

2. a=14, b=64, c=90, d=20, e=76 → c=90 wrong, e=76 wrong

3. a=14, b=76, c=64, d=90, e=20 → all wrong

4. a=14, b=64, c=76, d=20, e=90 → this would be correct. Wait maybe the user's second option has a typo, but looking at the options, the second option is "a=14, b=64, c=90 d=20, e=76" → no. Wait, maybe I made a mistake. Wait girls' <8 lbs: total girls is 96, girls ≥8 lbs is 20, so girls <8 lbs is 96 -20=76. So c=76. Total <8 lbs is a + c =14 +76=90, so e=90. So the correct option is the one with a=14, b=64, c=76, d=20, e=90. Looking at the options, the fourth option (if the user's last option is that) but the user's options:

Wait the user's options:

○ a=64, b=14, c=76, d=20, e=90

○ a=14, b=64, c=90 d=20, e=76

○ a=14, b=76, c=64, d=90, e=20

○ a=14, b=64, c=76, d=20, e=90 → this is the correct one. So the answer is the fourth option (if the last option is that), but looking at the options, the second option is "a=14, b=64, c=90 d=20, e=76" → no, c should be 76, e=90. Wait, maybe the user's second option has a typo, but according to the calculation, a=14, b=64, c=76, d=20, e=90. So the correct option is the one with these values.

Answer:

a=14, b=64, c=76, d=20, e=90 (the fourth option, assuming the last option is this)