Help Pleaseeeeeeeee
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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
Re: Help Pleaseeeeeeeee ‼️‼️
0.875x-48=0.363xfluffygirl_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
0.512x=48
x = 93.75
the same as 7/8*x - 48 = 4/11*x
hope it helps
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!)
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!)
Re: Help Pleaseeeeeeeee ‼️‼️
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.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!)
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
Re: Help Pleaseeeeeeeee ‼️‼️
O, yes, you’re rightAdamV 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
Re: Help Pleaseeeeeeeee
Ratio before Jill gave out money is 7/8 meaning Jill had 7 portion and Jack had 8. Total portion was 7+8=15fluffygirl_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
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.
Re: Help Pleaseeeeeeeee
That was quicker than my method - thanks!Qeb2019 wrote:Ratio before Jill gave out money is 7/8 meaning Jill had 7 portion and Jack had 8. Total portion was 7+8=15fluffygirl_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
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.
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- Joined: Sun Mar 17, 2019 9:29 pm
Re: Help Pleaseeeeeeeee
Thank you everyone