Question

Meiling and Meimei divide $69 into 2 shares. `3/4` of Meiling's share is equal to `2/5` of Meimei's share. How much does each get?

Answer 1

This solution will require two equations with two variables. Read on...

Explanation:

Let x represent Meiling's share and y represent Meimei's share. The first sentence allows us to write

x + y = 69

The second sentence can be written as

`3/4 x = 2/5 y`

There are a couple of ways to proceed from here. The one I like best is to multiply the second equation by `5/2` to change the coefficient of y into a 1.

`5/2` x `3/4 x = y`

`15/8` x = y

Now, replace the y in equation 1 with this expression

x + `15/8`x = 69

Now, we have only one equation in one unknown and we can solve it (hopefully)

`23/8`x = 69

Multiply both sides by `8/23`

x = 69 x `8/23`

x = 24

So, y = 45 (based on the first equation.