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Urgent help with GCSE Maths Question

Fabio has a large jar containing only black and green olives. The probability of a randomly choosing a black olive from the jar is 5 ∕16.After eating 1 green and 3 black olives the probability of choosing a black olive is 3∕10. How many black and green olives were originally
in the jar?

Please help i dont know how to start this question

I know you have to take ratio but thats as far as ive got
(edited 6 years ago)
Original post by Rockyboy
Fabio has a large jar containing only black and green olives. The probability of a randomly choosing a black olive from the jar is 5 ∕16.After eating 1 green and 3 black olives the probability of choosing a black olive is 3∕10. How many black and green olives were originally
in the jar?

Please help i dont know how to start this question

I know you have to take ratio but thats as far as ive got

bb+g=516\frac{b}{b+g}=\frac{5}{16}

b3b3+g1=310\frac{b-3}{b-3+g-1}=\frac{3}{10}

Continue
Reply 2
Original post by RogerOxon
bb+g=516\frac{b}{b+g}=\frac{5}{16}

b3b3+g1=310\frac{b-3}{b-3+g-1}=\frac{3}{10}

Continue


Can you explain how you got those equations please
Original post by Rockyboy
Can you explain how you got those equations please

The probability of picking a black olive is the number of black olives divided by the total number of olives, i.e. bb+g\frac{b}{b+g}.

Once 3 black and 1 green olive have been eaten, we have the same equation, but with b=b3b'=b-3 and g=g1g'=g-1, equaling 310\frac{3}{10}.

Please try to work it out before looking at this:

Spoiler

(edited 6 years ago)
Original post by RogerOxon
bb+g=516\frac{b}{b+g}=\frac{5}{16}

b3b3+g1=310\frac{b-3}{b-3+g-1}=\frac{3}{10}

Continue


A little more:

bb+g=516\frac{b}{b+g}=\frac{5}{16}

16b=5(b+g)\therefore 16b=5(b+g)

b+g=165b\therefore b+g=\frac{16}{5}b

b3b3+g1=310\frac{b-3}{b-3+g-1}=\frac{3}{10}

10(b3)=3(b+g4)=3(b+g)12\therefore 10(b-3)=3(b+g-4)=3(b+g)-12

10b18=3(b+g)=485b\therefore 10b-18=3(b+g)=\frac{48}{5}b

50b90=48b\therefore 50b-90=48b

etc
Original post by RogerOxon
bb+g=516\frac{b}{b+g}=\frac{5}{16}

b3b3+g1=310\frac{b-3}{b-3+g-1}=\frac{3}{10}

Continue

b is 45, just equal the equations and rearrange.

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