Question

the ratio of students to adults on a field trip is 49 to 7. which table correctly represents this ratio? a students adults 49 7 56 14 63 21 b students adults 7 1 8 2 9 3 c students adults 49 7 56 8 63 9 d students adults 7 1 14 8 21 15

Explanation:

Step1: Simplify the given ratio

The ratio of students to adults is \( 49:7 \). Simplify this ratio by dividing both numbers by their greatest common divisor, which is 7. So, \( \frac{49}{7}:\frac{7}{7} = 7:1 \). Now we can check each table to see if the ratio of students to adults is \( 7:1 \) (or equivalent, since ratios can be scaled by multiplying both parts by the same number).

Step2: Check Table A

• First row: \( 49:7 = 7:1 \) (divided by 7)
• Second row: \( 56:14 \). Simplify by dividing both by 14: \( \frac{56}{14}:\frac{14}{14} = 4:1 \). This is not \( 7:1 \), so Table A is incorrect.

Step3: Check Table B

• First row: \( 7:1 \) (correct)
• Second row: \( 8:2 \). Simplify by dividing both by 2: \( \frac{8}{2}:\frac{2}{2} = 4:1 \). This is not \( 7:1 \), so Table B is incorrect.

Step4: Check Table C

• First row: \( 49:7 = 7:1 \) (divided by 7)
• Second row: \( 56:8 \). Simplify by dividing both by 8: \( \frac{56}{8}:\frac{8}{8} = 7:1 \) (since \( 56 \div 8 = 7 \) and \( 8 \div 8 = 1 \))
• Third row: \( 63:9 \). Simplify by dividing both by 9: \( \frac{63}{9}:\frac{9}{9} = 7:1 \) (since \( 63 \div 9 = 7 \) and \( 9 \div 9 = 1 \))
• All rows in Table C have a ratio of \( 7:1 \), which is equivalent to the original ratio \( 49:7 \) (since \( 49:7 = 7:1 \), and scaling by 8 gives \( 56:8 \), scaling by 9 gives \( 63:9 \)).

Step5: Check Table D (for completeness)

• First row: \( 7:1 \) (correct)
• Second row: \( 14:8 \). Simplify by dividing both by 2: \( 7:4 \), which is not \( 7:1 \). So Table D is incorrect.

Answer:

C.

Students	Adults
56	8
63	9