Question

The ratio of students to adults on a field trip is 8 to 1. Which table correctly shows this ratio for each grade?

Answer 1

Table C is correct

Explanation:

Ratio or Proportion

When some quantity has a value M respect to another quantity of value N, we say the ratio between them is

`\displaystyle r=(M)/(N)`

That ratio (in absolute value) can be greater than one, if M>N, less than one if M<N or 1 if they are equal

The problem states the ratio of students to adults on a field trip is 8 to 1.

We need to search in each table in which one has the correct ratio for all grades. Let's test the first table

For 6th grade, the ratio of students to adults is

`\displaystyle r=(96)/(88)`

this is far away from 8, so this table is wrong

Now for the table C

For grade 6 the ratio is

`\displaystyle r=(96)/(12)=8`

For grade 7

`\displaystyle r=(120)/(15)=8`

For grade 8

`\displaystyle r=(136)/(17)=8`

Since all the ratios are 8, this is the correct answer.

Answer 2

The table C correctly shows the ratio 8:1 for each grade

Explanation:

Let

x ----> the number of students

y ----> the number of adults

we know that

`(x)/(y)=(8)/(1)`

Verify each table

Table A

grade 6

`(96)/(88)=(8)/(1)`

Multiply in cross

`96(1)=8(88)` ----> is not true

Table B

grade 6

`(96)/(104)=(8)/(1)`

Multiply in cross

`96(1)=8(104)` ----> is not true

Table C

grade 6

\frac{96}{12}=\frac{8}{1}

Multiply in cross

`96(1)=8(12)`

`96=96` ----> is true

grade 7

`(120)/(15)=(8)/(1)`

Multiply in cross

`120(1)=8(15)`

`120=120` ----> is true

grade 8

\frac{136}{17}=\frac{8}{1}

Multiply in cross

`136(1)=8(17)`

`136=136` ----> is true

therefore

The table C correctly shows the ratio 8:1 for each grade

Table D

grade 6

`(96)/(11)=(8)/(1)`

Multiply in cross

`96(1)=8(11)`----> is not true