Question

the ratio of fifth graders to sixth graders is 4 to 5 if one of the graders totals is 160 select the possible totals for the other grade A. 32B. 40C. 128D. 160 E. 200

Answer 1

Answers:

C. 128

E. 200

Step-by-step explanation:

We have two options, there are 160 students in fifth grade or there are 160 students in sixth grade

If there are 160 students in fifth grade, we can formulate the following proportion:

`(fifth)/(sixth)=(4)/(5)=(160)/(x)`

Where x is the total for the other grade (sixth grade). So, solving for x, we get:

`\begin{gathered} (4)/(5)=(160)/(x) \\ 4\cdot x=160\cdot5 \\ 4\cdot x=800 \\ x=(800)/(4) \\ x=200 \end{gathered}`

So, one of the answers is 200

On the other hand, if there are 160 students in sixth grade, the proportion is equal to:

`\frac{\text{fifth}}{\text{sixth}}=(4)/(5)=(y)/(160)`

Where y is the total for the other grade (fifth grade). So, solving for y, we get:

`\begin{gathered} (4)/(5)=(y)/(160) \\ (4)/(5)\cdot160=(y)/(160)\cdot160 \\ 128=y \end{gathered}`

So, the other answer is 128

Therefore, the answers are C. 128 and E. 200