Question

the ratio of Simone's pocket money to Fiona's pocket money was 2:3. After Fiona had received $5 from her mother, the ratio of Simone's pocket money to Fiona's pocket money became 4:7. how much pocket money did both of them have at first?

Answer 1

s = 2 f/3

s = 4 (f+5) /7

--------------------
2 f/3 = 4 f/7 + 20/7

2*21 f/3 = 4*21 f/7 + 20*21 /7

14 f = 12 f + 60

2 f = 60
so
f = 30
s = 2 f/3 = 20
=======================
check
s/f = 20/30 = 2/3 yes

s/(f+5) = 20/35 = 4/7 yes, it worked

Answer 2

how about this approach:

Simone's money --- 2x
Fiona's money --- 3x

after mom's gift:
2x/(3x+5) = 4/7
14x = 12x + 20
2x = 20
x = 10

so Simone had 2x or $20
Fiona had 3x or $30