Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    19
    ReputationRep:
    Name:  Maths New.jpg
Views: 58
Size:  300.8 KB

    How do you work out this question?
    The answer is 42 apparently and it does work if you use the information given and substitute the values into the answer.
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Chittesh14)
    Name:  Maths New.jpg
Views: 58
Size:  300.8 KB

    How do you work out this question?
    The answer is 42 apparently and it does work if you use the information given and substitute the values into the answer.
    The number of yellow balls is an unknown so let's call that n.

    Then the number of red balls is n+6

    So the ratio of red balls to yellow balls is n+6:n

    Now work out how these expressions change when the balls are removed. And then write down the new ratio.

    Please post all your working if you get stuck.
    Offline

    22
    ReputationRep:
    (Original post by Chittesh14)
    ...
    Call the number of red balls x, then:

    \displaystyle

\begin{equation*} \frac{x}{x-6} = \frac{x-4}{x-6-3} \end{equation*}

    Solve this equation/quadratic/linear equation for x, take away 6 for the number of yellow, then add those two numbers to get the total.
    • Thread Starter
    Offline

    19
    ReputationRep:
    (Original post by Zacken)
    Call the number of red balls x, then:

    \displaystyle

\begin{equation*} \frac{x}{x-6} = \frac{x-4}{x-6-3} \end{equation*}

    Solve this equation/quadratic/linear equation for x, take away 6 for the number of yellow, then add those two numbers to get the total.
    Thanks lol :P.
    I don't know why I kept making mistakes, I obviously knew how to approach the question but for some reason I kept getting:

    \displaystyle

\begin{equation*} \frac{x}{x-6} = \frac{x-4}{x-1} \end{equation*}

    or even:

    \displaystyle

\begin{equation*} \frac{x}{x-6} = \frac{x-4}{x-5} \end{equation*}

    I kept doing this:

    at the start red balls = x
    yellow balls = x-6

    Afterred balls = x-4
    4 less red balls, so y = x - 2
    then 3 yellow balls were removed so yellow balls = x - 5

    Spoiler:
    Show
    Anyway, the way to work it out for anyone else who might want to know:

    \displaystyle

\begin{equation*} \frac{x}{x-6} = \frac{x-4}{x-9} \end{equation*}

    x(x-9) = (x-6)(x-4)

x^2-9x = x^2 - 10x + 24

0 = -x + 24

x = 24



The x refers to the number of red balls in the bag.



To solve for how many yellow balls there were originally, you just use the information given at first.

There were 6 more red balls than yellow, so if y = yellow and x = red.

x = y + 6

and therefore y = x - 6, in this case y = 24 - 6 = 18.



Originally, there were 24 + 18 = 42 balls in the bag.
    • Thread Starter
    Offline

    19
    ReputationRep:
    (Original post by notnek)
    The number of yellow balls is an unknown so let's call that n.

    Then the number of red balls is n+6

    So the ratio of red balls to yellow balls is n+6:n

    Now work out how these expressions change when the balls are removed. And then write down the new ratio.

    Please post all your working if you get stuck.
    Thank you for your help. I've solved the question now.
    But, I was just wondering, would this method be correct too?

    Red balls = r

    \displaystyle

\begin{equation*} \frac{r}{r-6} = \frac{4}{3} \end{equation*}

    Where, 4 = number of red balls removed and 3 = number of yellow balls removed.

    Because, if 4 red balls were removed and 3 yellow balls were removed and the ratio at the start and after the balls were removed stays the same, then that must be the ratio 4:3.

    Since,

    \displaystyle

\begin{equation*} \frac{r}{r-6} = \frac{4}{3} \end{equation*}

    3r = 4r - 24
    24 = r

    number of yellow balls = number of red balls - 6 balls
    y = r - 6

    Then, substitute it in:

    Total = t.
    Total = number of red balls + number of yellow balls
    Total = r + r - 6
    Total = 24 + (24-6) = 24 + 18 = 42.

    24 red balls
    18 yellow balls
    total = 42 balls

    If you check it:

    \displaystyle

\begin{equation*} \frac{24}{18} = \frac{4}{3} \end{equation*}

    24:18 = ratio 4:3

    After 4 red balls are removed and 3 yellow balls are removed, 20:15 = 4:3.

    \displaystyle

\begin{equation*} \frac{20}{15} = \frac{4}{3} \end{equation*}

    Ratio is same - answer is correct.

    Method?
    Offline

    22
    ReputationRep:
    Oh darn, I didn't see Notnek's post! Sorry!
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Chittesh14)
    Thank you for your help. I've solved the question now.
    But, I was just wondering, would this method be correct too?
    Yes your method is correct.

    If you have a ratio x:y and you add a to x and b to y to keep the ratio the same then a:b = x:y.


    \displaystyle \frac{x}{y} = \frac{x+a}{y+b}

    \displaystyle \Rightarrow xy + bx = xy + ay \Rightarrow bx = ay

    \displaystyle \Rightarrow \frac{x}{y} = \frac{a}{b}
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.