Milly Miffin made one muffin more than Molly’s mother made, and Milly Miffin’s mother made one muffin more than Molly made; and Molly’s mother and Milly and Milly’s mother and Molly made 50 muffins (total), but Molly’s mother and Milly made 4 muffins more than Milly’s mother and Molly made. So murmur how many muffins Milly made.

Let

A = the number of Milly’s muffins

B = the number of Molly’s mother’s muffins

C = the number of Milly’s mother’s muffins

D = the number of Molly’s muffins

A = the number of Milly’s muffins

B = the number of Molly’s mother’s muffins

C = the number of Milly’s mother’s muffins

D = the number of Molly’s muffins

We have

A – 1 = B

C – 1 = D.

C – 1 = D.

(I) A + B + C + D = 50

Using substitution we see:

A + (A – 1) + C + (C – 1) = 50

2A – 1 + 2C – 1 = 50

2A + 2C = 52

A + C = 26

A = 26 – C

2A – 1 + 2C – 1 = 50

2A + 2C = 52

A + C = 26

A = 26 – C

(II) Then, A + B – 4 = C + D

Using substitution we see:

A + (A – 1) – 4 = C + (C -1)

(26 – C) + (26 – C – 1) – 4 = C + C – 1

26 – C + 26 – C – 1 – 4 = 2C – 1

52 – 2c – 5 = 2c – 1

47 – 2C = 2C – 1

48 = 4C

C = 12.

(26 – C) + (26 – C – 1) – 4 = C + C – 1

26 – C + 26 – C – 1 – 4 = 2C – 1

52 – 2c – 5 = 2c – 1

47 – 2C = 2C – 1

48 = 4C

C = 12.

Then,

A = 26 – 12 = 14,

B = A – 1 = 13,

and D = C – 1 = 11.

B = A – 1 = 13,

and D = C – 1 = 11.

So Milly made 14.

Check: (I) 14 + 13 + 12 + 11 = 50

and (II) 14 + 13 – 4 = 12 + 11