By algebra do you mean x and y ? Or units and parts?

I prefer units n parts

You do realise that units and parts is actually algebra ? Just not explicitly using x and y

Ya but i havent learnt algebra yet. So i think using parts is easier to understand

At first, Ratio of Jack to Milly = 5 : 1

That's 5 units to 1 unit.

In the end, Ratio of Jack to Milly = 3 : 1

That's 3 parts to 1 part.

For Milly, 1 unit + 4 = 1 part

For Jack, 5 units + 8 = 3 parts

But 3 parts also = 3 x (1 unit + 4)
= 3 units + 12


So this means :
5 units + 8 = 3 units + 12

Rewrite as :
3 units + 2 units + 8 = 3 units + 4 + 8

Comparing both sides,

2 units = 4

1 unit = 4 ÷ 2 = 2

Jack at first

= 5 units
= 5 x 2
= 10

Notice that it's the same when I replace units with x and parts with y :


For Milly, x + 4 = y ①

For Jack, 5x + 8 = 3y ②

But if I multiply ① by 3 on both sides,

3x + 12 = 3y

Now I substitute 3y = 3x + 12 into ② :

5x + 8 = 3x + 12

5x + 8 - 3x - 8 = 3x + 12 - 3x - 8

2x = 4

x = 2


Jack at first

= 5x
= 5 x 2
= 10