a ratio of 12:11. At this rate, how many students would turn in extra credit if there are a total of 200 students in the 7th grade?

Question

the number students turning in extra credit in 4th period is a ratio of 12:11. At this rate, how many students would turn in extra credit if there are a total of 200 students in the 7th grade?

Answer 1

Assuming your ratio values are correct, we can rewrite 

12:11 as a fraction 12/11 and interpret as....

 

EC means "Extra Credit"

12/11=(#students turning in EC) / (#students NOT turning in EC)

12+11=23.......total #students expressed in EC ratio

 

Rewrite students turning in EC as a ratio in terms of

total number of students (denominator)...

12:23::x:200....solve for "x"

 

Rewrite ratios as fractions and equate...

12/23=x/200....(#students turning in EC) / (total#students)

23x=12(200)....cross-multiply

23x=2400........simplify

∴ x=104.35.....divide both sides by 23

 

So with the "EC:not EC" ratio of 12:11, approximately 

104 students will turn in Extra Credit assignments.

 

If you set up "not EC:(total#students)" ratio of 11:23::x:200 

and solve in a similar manner, you will find that approximately 

96 students will NOT turn in Extra Credit assignments.

 

104+96=200 total students...√check, our calculated values

                                                    match the given total number

                                                    of students

 

 

 

 

 

 

Answer 2

12yes/11no ⇒ 12yes/23total = xyes/200total        now cross multiply

 

2400 = 23x

2400/23 = x

 

This is not a whole number which makes my assumptions suspect.

Is this all the information available?

Answer 3

The way the ratio is stated means that the first number (12) has to do with the number of students that turned in the extra credit. 11 is the part of the class that did not submit the extra credit.

If Y (y for yes) is the number of students who took the extra credit, and N (n for no) is the number of students who did not take the extra credit, we can set up a system of equations. Recall that the colon ':' symbol represents a division symbol (aka ratio).

First, we have the given ratio

Y/N = 12/11

This doesn't tell us much, since we have 1 equation and 2 unknowns. To find the other equation, we should consider that the problem tells us the total number of students in the class. We already defined Y and N as numbers of students, so we can write another equation.

Y + N = 200

Now we have 2 equations and 2 unknowns. We can solve this using the substitution method. Use the first equation to solve for Y

Y = (12/11)*N

Substitute this into the next equation and we get

(12/11)*N + N = 200

Now we have 2 terms with N in them. We want so solve for N, so what can we do to get N by itself? We factor N from those terms.

N * [ (12/11) + 1 ] = 200

Simplifying

N * (23/11) = 200

N = 95.65

 

This raises a flag, because there is no such thing as 0.65 of a student. We want whole numbers here.

 

Can you double-check the given information? This solutions applies to your problem, generally speaking, so you should be able to use it with your corrected numbers.

 

I hope this helped! Please ask any questions if you have them.