Anna baked some chicken and beef pies for her friends.45% of the chicken pies and 10% of the beef pies were eaten. Altogether 1/3 of the pies were eaten. In the end, she was left with 10 more chicken pies than beef pies. How many chicken pies did she bake? (Ans 100)


A very nice answer from alfretztay. I'm just adding some detail.

There is more than one way to do this question. We could do it with unit and parts; as a matter of fact, the question has clues which tell us to do just this. Like, more than one ratio is given, but they are ratios which add up to different numbers, not the same number.

So let's bite the bullet, and use units for the chicken pies and parts for the beef pies.

Chicken pies eaten : Chicken pies not eaten
45 : 55, which is the same as
9u : 11u

Beef pies eaten : Beef pies not eaten
10 : 90, which is the same as
1p : 9p

We're told that 1/3 of the pies were eaten; so 2/3 of the pies weren't. This gives us a bar model. I've colour-coded the units and parts to show what comes from where.

If you like bar models,
[Pies eaten][Pies eaten]
[.....Pies not eaten.....]

Pies eaten: 9u (chicken) + 1p (beef)
Pies not eaten: 11u (chicken) + 9p (beef)

And we know the ratio is 1 : 2 (a third of the pies were eaten).
[Pies eaten][Pies eaten] = [Pies not eaten]
9u + 1p + 9u + 1p = 11u + 9p

Adding up the units and parts on the left hand side:
18u + 2p = 11u + 9p

Units on the left, and parts on the right:
18u - 11u = 9p - 2p
7u = 7p

Which means 1 unit = 1 part, and it's all downhill from here. We're told that there were 10 more chicken pies left over than beef pies.
11u (chicken) - 9p = 10

And since 1 unit is exactly the same as 1 part, 9p is the same as 9u, so
11u - 9u = 10 =>2u = 10,
giving u = 5

Total number of chicken pies: 9u (eaten) + 11u (not eaten) = 20u.
As u is 5, Anna made 20 * 5 = 100 chicken pies.