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