Question

6 Luiz, Seth and Fran share £1440 in the ratio 3:5:7. Fran splits her share with her sister Ali in the ratio 4:1.

a) How much does each person end up with?
b) Find the ratio of the amount that Fran ends up with to the amount that Seth ends up with.
Give your answer in its simplest form.

Answer 1

Explanation:

Since we don't know how much each one of them gets, we will call that unknown amount x. Luiz gets 3x of the total amount, Seth gets 5x of the total amount, and Fran gets 7x of the total amount. The total amount is 1440, so the equation to find out how much that unknown amount x is looks like this:

3x + 5x + 7x = 1440 and

15x = 1440 so

x = 96.

That means that Luiz gets 3(96) = 288,

Seth gets 5(96) = 480,

and Fran gets 7(96) = 672. But Fran shares her portion in the ratio 4:1 with her sister. That's a separate equation that looks like this:

4x + 1x = 672 and

5x = 672 so

x = 134.40

That means that Ali gets 134.40, leaving Fran with 537.60.

That answers a. Now for b, the ratio of Fran's portion (what she's left with, at least) to Seth's is the fraction

`(537.60)/(480)=(28)/(25)` or in decimal form, 1.12

Answer 2

A) £1440 in the ratio of 3:5:7 is - £288: £480: £672

After Fran gives her sister Ali a share in the ratio 4:1, Fran was left with £537.60 and her sister was left with £134.40

B) Fran to Seth = £537.60: £480 → £28: £25

Explanation:

To find 1 part of £1440 in the ratio of 3:5:7 you have to add 3+5+7= 15

Then you divide £1440 by 15 which is = £96

Next you take 96 and times it by 3 then 5 then 7 and put it in the ratio 3:5:7= £288: £480: £672

To find out how much Fran and her sister Ali end up with you have to add 4 & 1 = 5

Then divide Fran’s share, £672, by 5= £134.40

£134.40 is Ali’s share and now we need to find Fran’s by multiplying £134.40 by 4 which is= £537.60

F: A = £537.60: £134.40

As we now know Fran is left with £537.60 and we have to put that into a ratio with what Seth has. Earlier we found out that Seth has a total of £480 from the original share (£1440). If we put this knowledge into a ratio it becomes:

£537.60: £480

But we need to simplify them. So we need to change the values to whole number.

Convert any decimal numbers to integers by multiplying both sides by 101 = 10 to eliminate all, 1, decimal places. We then have: 480: 537.6 = 4800: 5376

Try to reduce the ratio further with the highest common factor (HCF). The HCF in our case is 192.

We need to divide both terms by the HCF:

4800 ÷ 192= 25

5376 ÷ 192= 28