Question

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. which of these tables best represents the data? three tables are shown with options, each with rows for boys, girls, total and columns for < 8 lbs, ≥ 8 lbs, total, with some cells filled and others blank.

Explanation:

Step1: Calculate number of girls

Total babies = 160. Girls = $\frac{3}{5} \times 160 = 96$. So boys = $160 - 96 = 64$? Wait, no, wait. Wait, first, total babies 160. Girls: $\frac{3}{5}$ of 160 is $160\times\frac{3}{5}=96$. So boys total is $160 - 96 = 64$? Wait, no, the second table: boys total is 60? Wait, maybe I miscalculated. Wait, the problem says: 70 babies weighed 8 pounds or more. Fifty boys weighed 8 pounds or more. So let's build the table.

First, total babies: 160.

Girls total: $\frac{3}{5} \times 160 = 96$. So boys total: $160 - 96 = 64$? Wait, no, the second table has boys total 60. Wait, maybe I made a mistake. Wait, let's check the tables.

Let's list the data:

- Total babies: 160.

- Girls: $\frac{3}{5} \times 160 = 96$ (so girls total is 96).

- Boys: $160 - 96 = 64$? Wait, but the second table has boys total 60. Wait, maybe the problem has a typo, or I misread. Wait, the second table: boys total is 60? Wait, no, let's check the weight data.

Seventy babies weighed 8 pounds or more (≥8 lbs). Fifty boys weighed ≥8 lbs. So girls ≥8 lbs: $70 - 50 = 20$.

Now, boys total: let's see the tables. The third table: girls total is 96 (matches $\frac{3}{5}$ of 160). Total ≥8 lbs: 70 (matches). Boys ≥8 lbs: 50 (matches). Let's check the third table:

- Boys: ≥8 lbs: 50. So boys <8 lbs: boys total - 50. But boys total: 160 - 96 = 64? Wait, no, the third table: girls total is 96, so boys total is 160 - 96 = 64. Then boys <8 lbs: 64 - 50 = 14.

Girls: total 96. Girls ≥8 lbs: 70 - 50 = 20. So girls <8 lbs: 96 - 20 = 76.

Total <8 lbs: 160 - 70 = 90. Let's check the third table: total <8 lbs is 90 (since total is 160, ≥8 lbs is 70, so <8 lbs is 160 - 70 = 90).

Now, let's check each table:

First table:

- Boys: <8 lbs: 50. But boys total would be 50 + (≥8 lbs). But ≥8 lbs for boys is 50? No, first table has boys <8 lbs:50, ≥8 lbs:? Total boys:? Girls total:96. Total ≥8 lbs:70. Total:160. Doesn't match.

Second table:

- Boys: ≥8 lbs:50, total boys:60. So boys <8 lbs:60 - 50 = 10. Total <8 lbs:70. So girls <8 lbs:70 - 10 = 60. Girls total:96? No, 60 (girls <8 lbs) + girls ≥8 lbs (70 - 50 =20) =80 ≠96. So second table is wrong.

Third table:

- Girls total:96 (matches $\frac{3}{5}$ of 160).

- Total ≥8 lbs:70 (matches).

- Boys ≥8 lbs:50 (matches).

- Girls ≥8 lbs:70 -50=20.

- Boys total:160 -96=64. So boys <8 lbs:64 -50=14.

- Girls <8 lbs:96 -20=76.

- Total <8 lbs:14 +76=90 (which is 160 -70=90, correct).

So the third table (the rightmost one) has:

- Boys: ≥8 lbs:50, total boys:64 (160-96), so <8 lbs:14.

- Girls: total 96, ≥8 lbs:20, <8 lbs:76.

- Total <8 lbs:14+76=90, total ≥8 lbs:50+20=70, total:160. Correct.

Wait, but the third table's structure:

Columns: <8 lbs, ≥8 lbs, Total>

Rows: Boys, Girls, Total.

Boys row: <8 lbs:?, ≥8 lbs:50, Total:?

Girls row: <8 lbs:?, ≥8 lbs:?, Total:96

Total row: <8 lbs:?, ≥8 lbs:70, Total:160

So let's fill it:

Boys total: 160 - 96 = 64. So boys ≥8 lbs:50, so boys <8 lbs:64 -50=14.

Girls ≥8 lbs:70 -50=20. So girls <8 lbs:96 -20=76.

Total <8 lbs:14 +76=90.

Total ≥8 lbs:50 +20=70.

Total:90 +70=160.

So the third table (the rightmost one) has:

Boys: <8 lbs:14, ≥8 lbs:50, Total:64

Girls: <8 lbs:76, ≥8 lbs:20, Total:96

Total: <8 lbs:90, ≥8 lbs:70, Total:160

Which matches all data. So the correct table is the third one (the rightmost graph).

Step2: Verify with each table

- First table: Boys <8 lbs:50, but boys total would be 50 + (≥8 lbs). But girls total is 96, so boys total is 64. 50 + (≥8 lbs)=64 → ≥8 lbs=14, but total ≥8 lbs is 70, so girls ≥8 lbs=70 -14=56. But girls total is 96, so girls <8 lbs=96 -56=40. Total <8 lbs=50 +40=90, which is correct (160-70=90). Wait, but first table's total ≥8 lbs is 70, boys ≥8 lbs:? Wait, first table: boys <8 lbs:50, girls <8 lbs:?, girls total:96, total <8 lbs:?, total ≥8 lbs:70, total:160. Let's recalculate.

Total <8 lbs:160 -70=90. So boys <8 lbs + girls <8 lbs=90. Boys <8 lbs=50, so girls <8 lbs=40. Girls total=96, so girls ≥8 lbs=96 -40=56. Total ≥8 lbs=boys ≥8 lbs +56=70 → boys ≥8 lbs=14. So boys total=50 +14=64. Which is 160 -96=64. So first table: boys <8 lbs:50, ≥8 lbs:14, total:64. Girls <8 lbs:40, ≥8 lbs:56, total:96. Total <8 lbs:50 +40=90, ≥8 lbs:14 +56=70, total:160. But the first table's boys ≥8 lbs cell is empty, girls ≥8 lbs cell is empty, total <8 lbs cell is empty. So the first table has boys <8 lbs:50, girls total:96, total ≥8 lbs:70, total:160. But the second table: boys total:60, which is wrong. The third table: girls total:96, total ≥8 lbs:70, boys ≥8 lbs:50. Let's check the third table's structure:

Third table:

Rows: Boys, Girls, Total

Columns: <8 lbs, ≥8 lbs, Total

Boys: ≥8 lbs:50, Total:?

Girls: Total:96

Total: ≥8 lbs:70, Total:160

So boys total:160 -96=64. So boys <8 lbs:64 -50=14.

Girls ≥8 lbs:70 -50=20. So girls <8 lbs:96 -20=76.

Total <8 lbs:14 +76=90.

Which matches. Now, the first table: boys <8 lbs:50, which would mean boys total=50 + (≥8 lbs). But boys total should be 64, so ≥8 lbs=14. But the first table's boys ≥8 lbs cell is empty, and the third table's boys ≥8 lbs cell is 50 (which is correct, as 50 boys weighed ≥8 lbs). Wait, the problem says "Fifty boys weighed 8 pounds or more". So boys ≥8 lbs=50. So that's a key point. So boys ≥8 lbs=50. So in the table, the boys' ≥8 lbs cell should be 50. So let's check the tables:

First table: boys <8 lbs:50, ≥8 lbs:? (should be 50, but 50 +50=100, which is more than boys total 64. So first table is wrong.

Second table: boys ≥8 lbs:50, total boys:60. So boys <8 lbs:10. Total <8 lbs:70, so girls <8 lbs:60. Girls total:60 + (girls ≥8 lbs)=96 → girls ≥8 lbs=36. But total ≥8 lbs:50 +36=86≠70. So second table is wrong.

Third table: boys ≥8 lbs:50 (matches "Fifty boys..."), girls total:96 (matches $\frac{3}{5}$ of 160), total ≥8 lbs:70 (matches "Seventy babies..."), total:160 (matches). So the third table (the rightmost one) is correct.

Answer:

The Right Graph (the third table from the left, or the rightmost table)