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Help Pleaseeeeeeeee
https://www.elevenplusexams.co.uk/forum/11plus/viewtopic.php?f=2&t=57943
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Author:  fluffygirl_27 [ Tue May 07, 2019 6:26 pm ]
Post subject:  Help Pleaseeeeeeeee

The amount of money Jill had was 7/8 of the money Jack had. After giving £48 to Jack, Jill had 4/11 of Jack’s money. How much money did Jack have at first

Author:  dreams [ Tue May 07, 2019 9:15 pm ]
Post subject:  Re: Help Pleaseeeeeeeee ‼️‼️

fluffygirl_27 wrote:
The amount of money Jill had was 7/8 of the money Jack had. After giving £48 to Jack, Jill had 4/11 of Jack’s money. How much money did Jack have at first ❓❓


0.875x-48=0.363x
0.512x=48
x = 93.75

the same as 7/8*x - 48 = 4/11*x

hope it helps

Author:  solimum [ Tue May 07, 2019 9:57 pm ]
Post subject:  Re: Help Pleaseeeeeeeee ‼️‼️

Not sure if that works - I'd keep it as fractions and avoid working out any arithmetic until the last possible moment:

Jill = 7/8 * Jack , or 8*Jill = 7*Jack

(Jill - 48) = 4/11 * (Jack + 48) - rewrite as 11 * (Jill - 48) = 4 * (Jack + 48)

Replace Jill in the second equation with 7/8 * Jack and remove brackets (and avoid multiplying out the constants yet!)

11 * 7/8 * Jack - 11*48 = 4*Jack + 4*48

Collect the Jacks on one side and the constants on the other side

Jack * (77/8 - 4) = 48*(11+4)

Simplify - keeping the LHS as improper fractions over the same denominator

Jack * (77/8 - 32/8) = 48 * 15

Or even more simply:

Jack * 45/8 = 48 * 15

Factorize the RHS differently noting that 45 = 3 * 15

Jack * 45/8 = 16 * 3 * 15

Divide both sides by 45, multiply by 8

Jack = 16 * 8 = £128 so therefore Jill = 7/8 * £128 = £112

Phew!

(Jill woz robbed if you ask me!)

Author:  dreams [ Tue May 07, 2019 11:34 pm ]
Post subject:  Re: Help Pleaseeeeeeeee ‼️‼️

solimum wrote:
Not sure if that works - I'd keep it as fractions and avoid working out any arithmetic until the last possible moment:

Jill = 7/8 * Jack , or 8*Jill = 7*Jack

(Jill - 48) = 4/11 * (Jack + 48) - rewrite as 11 * (Jill - 48) = 4 * (Jack + 48)

Replace Jill in the second equation with 7/8 * Jack and remove brackets (and avoid multiplying out the constants yet!)

11 * 7/8 * Jack - 11*48 = 4*Jack + 4*48

Collect the Jacks on one side and the constants on the other side

Jack * (77/8 - 4) = 48*(11+4)

Simplify - keeping the LHS as improper fractions over the same denominator

Jack * (77/8 - 32/8) = 48 * 15

Or even more simply:

Jack * 45/8 = 48 * 15

Factorize the RHS differently noting that 45 = 3 * 15

Jack * 45/8 = 16 * 3 * 15

Divide both sides by 45, multiply by 8

Jack = 16 * 8 = £128 so therefore Jill = 7/8 * £128 = £112

Phew!

(Jill woz robbed if you ask me!)


But 112-48 should be equal to 4/11 of Jack’s initial amount of money which is equal to 46 according to your equation.

Author:  AdamV [ Wed May 08, 2019 7:48 am ]
Post subject:  Re: Help Pleaseeeeeeeee ‼️‼️

No, after Jill gives Jack £48 she has 4/11 of what Jack has now. Which is £48 more than he started with. So £112 - £48 = 4/11 of (128+48) = 4/11 of 176 = 4*16 = 64

Author:  dreams [ Wed May 08, 2019 7:55 am ]
Post subject:  Re: Help Pleaseeeeeeeee ‼️‼️

AdamV wrote:
No, after Jill gives Jack £48 she has 4/11 of what Jack has now. Which is £48 more than he started with. So £112 - £48 = 4/11 of (128+48) = 4/11 of 176 = 4*16 = 64

O, yes, you’re right

Author:  Qeb2019 [ Wed May 08, 2019 10:43 am ]
Post subject:  Re: Help Pleaseeeeeeeee

fluffygirl_27 wrote:
The amount of money Jill had was 7/8 of the money Jack had. After giving £48 to Jack, Jill had 4/11 of Jack’s money. How much money did Jack have at first


Ratio before Jill gave out money is 7/8 meaning Jill had 7 portion and Jack had 8. Total portion was 7+8=15

After Jill gave £48 new ratio is 4/11 ( total still 15 portion), easy to see that: Jill reduced 3 portion and Jack increase 3 portion and 3 portion is equal £48 therefore 1 portion is 48/3=16. Jack had 8x16=128.

Hope that helps.

Author:  solimum [ Wed May 08, 2019 3:00 pm ]
Post subject:  Re: Help Pleaseeeeeeeee

Qeb2019 wrote:
fluffygirl_27 wrote:
The amount of money Jill had was 7/8 of the money Jack had. After giving £48 to Jack, Jill had 4/11 of Jack’s money. How much money did Jack have at first


Ratio before Jill gave out money is 7/8 meaning Jill had 7 portion and Jack had 8. Total portion was 7+8=15

After Jill gave £48 new ratio is 4/11 ( total still 15 portion), easy to see that: Jill reduced 3 portion and Jack increase 3 portion and 3 portion is equal £48 therefore 1 portion is 48/3=16. Jack had 8x16=128.

Hope that helps.


That was quicker than my method - thanks!

Author:  fluffygirl_27 [ Wed May 08, 2019 7:04 pm ]
Post subject:  Re: Help Pleaseeeeeeeee

Thank you everyone

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