Weighting

[Grace20]

Can someone please help me with the following question:

A GCSE subject has two components. Component A coursework is worth 25 % and B is worth 75 % which is the final examination. A mark of 60 overall is needed for a grade C. A candidate scores 50/63 for coursework. The final exam is marked out of 110. What is the minimum mark the candidate needs to score on the final exam to gain a grade C?

 

[Deleted member 4993]

Can someone please help me with the following question:

A GCSE subject has two components. Component A coursework is worth 25 % and B is worth 75 % which is the final examination. A mark of 60 (is that out of 100?) overall is needed for a grade C. A candidate scores 50/63 for coursework. The final exam is marked out of 110. What is the minimum mark the candidate needs to score on the final exam to gain a grade C?

I'll do a similar but different problem:


A GCSE subject has two components. Component A coursework is worth 1/3 and B is worth 2/3 which is the final examination. A mark of 70% overall is needed for a grade C. A candidate scores 74/90 for coursework. The final exam is marked out of 150. What is the minimum mark the candidate needs to score on the final exam to gain a grade C?

course work 74 out 90 → (74/90 *100 = ) 82.22 %

So course-work will contribute (82.22/3 =) 27.407% towards final grade

Candidate needs to get (70 - 27.407 = ) 42.592% from final exam.

S/he must score (42.592 * 3/2) 63.889% in the final exam

Final exam is scored out of 150

Candidate must score at least (0.63889 * 150 = 95.8) 96 out 150 to score a C.

 

[Grace20]

Is this correct?

Component A: 25 %= 1/4 coursework



Component B= 75 % 3/4 exam



mark of 60 to pass



Here is the solution 50/64 *100= 78.125 % then divide by 4 = 19.53125%



60- 19.53125= 40.46875 %



40.46875 * 4/3 = 53.95833333/100= 0.539383333 *110 = 59.35



So the answer is 59/ 110 to get a C



Why do you change the fraction into an improper fraction ?

 

[soroban]

Hello, Grace20!

A GCSE subject has two components.
Component A (coursework) is worth 25%.
Component B (final exam) is worth 75%.
A mark of 60% overall is needed for a grade C.
A candidate scores 50/63 for coursework.
The final exam is marked out of 110.

What is the minimum mark the candidate needs
to score on the final exam to gain a grade C?

Let \(\displaystyle x\) = his final exam mark.
His score for the final exam is \(\displaystyle \frac{x}{110}\)
This counts 75% \(\displaystyle (\tfrac{3}{4})\) of his final grade.
This contributes \(\displaystyle \frac{3}{4}(\frac{x}{110}) \:=\:\frac{3x}{440}\) toward his final grade.

He scored \(\displaystyle \frac{50}{63}\) on coursework.
This counts 25% \(\displaystyle (\frac{1}{4})\) of his final grade.
This contributes \(\displaystyle \frac{1}{4}(\frac{50}{63}) \:=\:\frac{50}{252}\) toward his final grade.

Hence, his final grade is: .\(\displaystyle \frac{3}{440}x + \frac{50}{252}\)

But we want his final grade to be at least 60% \(\displaystyle (\frac{3}{5}).\)

We have: .\(\displaystyle \frac{3}{440}x + \frac{50}{252} \:\ge\:\frac{3}{5}\)

. . . . . . . . . . . . \(\displaystyle \frac{3}{440}x \;\ge\;\frac{3}{5} - \frac{50}{252} \;=\;\frac{253}{630} \)

. . . . . . . . . . . . . . . \(\displaystyle x \;\ge\;\frac{440}{3}(\frac{253}{630}) \;=\;58.8994709 \)


Therefore, he must score at least 59 points on his final exam.

 

[Deleted member 4993]

Is this correct?

Component A: 25 %= 1/4 coursework

Component B= 75 % 3/4 exam

mark of 60 to pass

Here is the solution 50/64 *100= 78.125 % then divide by 4 = 19.53125%

60- 19.53125= 40.46875 %

40.46875 * 4/3 = 53.95833333/100= 0.539383333 *110 = 59.35

So the answer is 59/ 110 (from your work it should be the minimum required score 60 ) to get a C

Let's check:

Component A → 50/64 → 78.125% → contribution towards final grade → 19.53125%

Component B → 59/110 → 53.636% → contribution towards final grade → 40.2273%

Final grade → 19.53125% + 40.2273% → 59.758 < 60%

Some grade calculators will call that < 60% - and hence not a 'C'.

But in your original post - the student scored 50/63 (not 50/64) and in that case 59 would be good enough!!

Why do you change the fraction into an improper fraction ?

Excellent work - as you can surmise from Soroban's response above that you got the correct answer.

However you asked:

Why do you change the fraction into an improper fraction ?

Where do you see that?

Thanks for sharing your final solution - lot of students will benefit from your work.