total: 5u
M: u
J: 4509.60-u
L: 5u-4509.60

4509.60-u = ½(u+5u-4509.60)
u = 1691.1

(a)
Lucy received (5x1691.1-4509.6)/8455.5 = 7/15 of total sum of money.

(b)
Lucy received (3945.90-1691.1) = $2254.80 more than Mary.

Thanks for helping. My daughter hasn't learn algebra yet. They are using model drawings which i am trying to learn it too.

u hv misunderstood.
the "u" here refers to unit.

ur daughter wld understand.
she wld know how to infer 5u means she wld draw 5 "boxes" in models.

Oic... how do u derive this
J=4509.6-u

the qn states that M & J received 4509.60.

M is one "box".

hence, u can mark an unknown length of "boxes"(approx. ) inclusive of M, and label it as 4509.60.

And the "boxes" within 4509.60 excl. of M is J.

L is total excl. 4509.60

A fractions approach :


a)Mary received 1/5 of total money.

Fraction of money Jane + Lucy had = 1 - 1/5 = 4/5

We know Jane received ½ of Mary + Lucy.

Here we can split Jane's money into two different parts : ½ of Mary's and ½ of Lucy's

½ of Mary = 1/5 of total x ½ = 1/10 of total

Subtract 1/10 from 4/5,

4/5 - 1/10 = 8/10 - 1/10 = 7/10

So this 7/10 of the total money is made up of Lucy's money and the rest of Jane's money

= Lucy + ½ Lucy's money
= 1½ of Lucy's money
= 3/2 of Lucy's money

7/10 of total = 3/2 of Lucy's
Lucy's = 7/10 of total x 2/3
= 7/15 of total


b)

Fraction that is Mary + Jane
= 1 - fraction that is Lucy's
= 1 - 7/15
= 8/15

8/15 of money = $4509.60


Lucy - Mary
= 7/15 of total - 1/5 of total
= 7/15 of total - 3/15 of total
= 4/15 of total

Since 8/15 of total = $4509.60,

4/15 of total is just ½ of that.

$4509.60 x ½ = $4509.60 ÷ 2
= $2254.80

Thank you all for your solutions.
- Ferlycia