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nordsb [41]
3 years ago
8

A leprechaun places a magic penny under a​ girl's pillow. The next night there are 2 magic pennies under her pillow. The followi

ng morning she finds four pennies.​ Apparently, while she sleeps each penny turns into two magic pennies. The total number of pennies seen under the pillow each day is the grand​ total; that​ is, the pennies from each of the previous days are not being stored away until more pennies magically appear. How many days would elapse before she has a total of more than ​$5 billion​? ​(Proceed by trial and​ error.)
nothing days
​(Type a whole​ number.)
Mathematics
1 answer:
vfiekz [6]3 years ago
7 0

Answer:

34

Step-by-step explanation:

Since the pennies need to be kept under the pillow in order to be doubled, we're really looking for the day the girl will wake up with 5 billion pennies under her pillow.

The general formula of that geometric sequence will be: t = 1 + 2^(n-1)

We need to find the value of n when t will be over 5,000,000,000.

So, the equation becomes:

5,000,000,001 = 1 + 2^(n-1)

2^{n-1}= 5,000,000,001

log(2^{n-1}) = log(5,000,000,000)

(n-1) * log(2) = log(5,000,000,000)

n-1 = log(5,000,000,000) / log(2)

n-1 = 22.25

n = 33.25

Since it has to be complete days, and we have to reach over 5 billion, then we round it up to 34.

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Answer: green shirts = 6

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Step-by-step explanation:

Red shirts = 7

Let green shirts be x.

There are 5 more blue shirts than green shirts. This means:

Blue shirts = x + 5

There are 2 fewer yellow shirts than green shirts. This means:

Yellow shirts = x - 2

There are 28 shirts in total

Red + blue + yellow + green = 28

7 + (x + 5) + (x - 2) + x = 28

7 + x + 5 + x - 2 + x = 28

10 + 3x = 28

3x = 28 - 10

3x = 18

x = 18/3

x = 6

There are 6 green shirts

Blue shirts = x + 5 = 6 + 5 = 11

Yellow shirts = x - 2 = 6 - 2 = 4

Red shirts = 7

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