11 Plus Exams Forum

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

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

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!)

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.

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

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

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.

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!

Thank you everyone