Before

D : E : F
3u : 1u : 8u ①

-$8|+$8 | -4u
□□|+4u |□□

(□ just represents blank space, ignore it)


After

D : E : F
1u : 3u : 2u

↓×2↓×2↓×2

2u : 6u : 4u ②

(We multiply by 2 because Francis would have 4u left after giving Erica half of his 8u at first. So we have to make his units the same)


Looking at ① and ② and comparing the ratio for Dominic, we see that :

3u - $8 = 2u

but 3u - $8 = 3u - 1u

So 1u = $8


Total they had at first

= 3u + 8u + 1u

= 12u

= 12 x $8

= $96

Your mistake was you didn't change the end ratio 1 : 3 : 2 to 2 : 6 : 4.

Notice that for Francis, 4u was taken away from 8u but the units at the end doesn't match up.

Likewise for Erica, 1u + $8 + 4u = 5u + $8

But the end ratio is only 3u, which itself is already less than 5u.

Alternatively, we can look at Erica's part of the ratio and see that :

1u + $8 + 4u = 6u

5u + $8 = 6u

5u + $8 = 5u + 1u

So 1u = $8

Then total they had at first

= 12u

= 12 x $8

= $96



This is a question from the 2019 CHIJ St Nicholas Girls' School (Primary)'s

Primary 6 SA1 Mathematics Paper 1 Booklet A