Either use units and parts (basically x and y in algebra, just switch the names to the former)

Or draw a model

Make the units the same for the girls for both ratios first.

Common multiple of 4 and 3 is 12


At first,
girls : boys = 4 : 3 = 12 : 9 (multiplied by 3)

After,
girls : boys = 3 : 4 = 12 : 16 (multiply by 4)



Since 188 girls left, we can say that :

12 units (after) + 188 = 12 parts (at first)


Divide by 4,
3 units (after) + 47 = 3 parts (at first)

Multiply by 3,
9 units (after) + 141 = 9 parts (at first) ①


9 parts is the number of boys at first.


Since 36 boys left, we can say that :

16 units (after) + 36 = 9 parts (at first) ②



Comparing ① and ② , this tells us that :


16 units (after) + 36 = 9 units (after) + 141



⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛⬛--36--|
⬛⬛⬛⬛⬛⬛⬛⬛⬛---------141--------------------|

So, 7 units = 141 - 36 = 105

1 unit = 105 ÷ 7 = 15


Children in the science centre in the afternoon

= 12 units + 16 units
= 28 units

= 28 × 15
= 420



Children in the science centre in the morning

= 420 + 188 + 36
= 644

any simplified methods ?

Is there any approach you're looking at in particular?

Usually for such 5m questions (Qn 17 or Qn 16 of Paper 2) , it's meant to be more challenging and even the model drawing will need some modifying.

Morning (Girls : Boys = 4 : 3)

Girls
47|47|47|47| → adds up to 188
+
3u|3u|3u|3u| → adds up to 12u

Boys
47|47|47|→ 141
+
3u|3u|3u| →9u

↓
↓ -188 girls , -36 boys
↓

Afternoon (Girls : Boys = 3 : 4)

Girls , Redraw 12u into :

4u|4u|4u| → adds up to 12u

Boys
4u|4u|4u|4u| → 16u


But, Boys also equals :
105 + 3u|3u|3u| → 105 + 9u

(Subtract 36 from the morning model)


So comparing the two,


16u and 105 + 9u are equal.


105 = 7u
1u = 15



Afternoon total = 12u + 16u = 28u

= 28 × 15
= 420


Morning Total = 420 + 36 + 188
= 644

Alternative way to draw :


Morning (Girls : Boys = 4 : 3)

Girls
12|12|12|12| → adds up to 48
+
4u|4u|4u|4u| → adds up to 16u

Boys
12|12|12|→ 36
+
4u|4u|4u| →12u

↓
↓ -188 girls , -36 boys
↓

Afternoon (Girls : Boys = 3 : 4)

Girls
3u|3u|3u|→ 9u

Boys, Redraw 12u into :
3u|3u|3u|3u| → 12u


Comparing the two models for girls,

Morning|12|12|12|12|4u|4u|4u|4u|
Aftnoon -----------188----------|3u|3u|3u|


16u - 9u = 7u
188 - 48 = 140

7u = 140
1u = 20



Afternoon total :

9u + 12u = 21u
= 21 × 20
= 420


Morning total

= 420 + 36 + 188
= 644