How many acorns did these chipmunks start with on monday morning?

Question

Chipper and Dalie collected 32 acorns on Monday and stored them in their acorn supply. After Chipper fell asleep, dalie ate half the acorns. This pattern continued through Friday night, with 32 acorns being added and half the supply being eaten. On sunday morning, chipper counted the acorns and found that they only had 35. How many acorns did they start with on Monday?

Answer 1

Ok, this is quite a tricky problem because you need to keep track of everything:  I'm going to try and break this down as much as i can.

On Monday morning, lets say the chipmunks have x acorns (we use x because it is unkwown)

They then collect 32 making thier collection x + 32

Chip then eats 1/2 of the collection (of means to multiply) so they now have:  (1/2)x + 16

Tuesday = (1/2)x + 16

After collecting 32 more = (1/2)x + 16 + 32 = (1/2)x + 48

Eats half of the collection = (1/2)(1/2x + 48) = (1/4)x + 24

Wednesday = (1/4)x + 24

After collecting 32 more = (1/4)x + 24 + 32 = (1/4)x + 56

Eats half of the collection = (1/2)(1/4x + 56) = (1/8)x + 28

Thursday = (1/8)x + 28

AFter collecting 32 more = (1/8)x + 28 +32 = (1/8)x + 60

Eats half of the collection = (1/2)(1/8x + 60) = (1/16)x + 30

Friday = (1/16)x + 30

After collecting 32 more = (1/16)x + 30 +32 = (1/16)x + 62

Eats hal of the collection = (1/2)(1/16x + 62) = (1/32)x + 31

Now we know they have 35

so:

(1/32)x + 31 = 35

(1/32)x  = 4

x = 128

so they started with 128 acorns.

Voila

Answer 2

Let:

n = number started with on Monday

For 5 days, they added 32, then ate half, until there were 35 total.

Day 1:

o = (n + 32)/2  // you'll see why I call this o later.  it will get ugly later if I don't

Day 2:

p = (o + 32)/2

Day 3:

q = (p + 32)/2

Day 4:

r = (q + 32)/2

Day 5:

s = (r + 32)/2

This is now equal to 35.  So let's start working backwards to find out what "n" was:

35 = (r + 32)/2

70 = r + 32

r = 38

r = (q + 32)/2

38 = (q + 32)/2

76 = q + 32

44 = q

q = (p + 32)/2

44 = (p + 32)/2

88 = p + 32

p = 56

p = (o + 32)/2

56 = (o + 32)/2

112 = o + 32

o = 80

o = (n + 32)/2

80 = (n + 32)/2

160 = n + 32

n = 128

They started with 128 Monday morning.