A band of 17 pirates stole a sack of gold coins. When they tried to divide the fortune into equal portions, 3 coins remained. In the ensuing brawl over who should get the extra coins, one pirate was killed. The wealth was redistributed, but this time an equal division left 10 coins. Again an argument developed in which another pirate was killed. But now the total fortune was evenly distributed among the survivors. What was the least number of coins that could have been stolen

Answers

Answer 1

Answer:

The least number of coins that could have been stolen is 3,930.

Step-by-step explanation:

In the beginning, there are N coins to be distributed among 17 pirates, and we know that if we divide evenly these coins, there are 3 coins remaining.

Then we can write the total number of coins as a multiple of 17 plus 3.

N = 17*k + 3

where k is an integer.

After that, a pirate is killed, so now we have 16 pirates, and now there are 10 coins left, so now we can write N as a multiple of 16 plus 10:

N = 16*j + 10

where j is an integer.

Finally, having 15 pirates, the total number of coins can be divided evenly, then N is a multiple of 15

N = 15*m

where m is an integer.

So we have these 3 equations:

N = 17*k + 3

N = 16*j + 10

N = 15*m

So we can express equations like:

15*m = 16*j + 10

15*m = 17*k + 3

Where we need to find solutions such that both of these variables are integers.

For the first one we can write:

15*m - 16*j = 10

One way to do it, is to write this like a linear equation:

m = (16*j + 10)/15

Graph this, and find the pairs of points in the line that have bot integer values, or we can just find some values of j such that:

16*j + 10 is a multiple of 15.

For example, with j = 5 we have:

m = (16*5 + 10)/15 = 6

so j = 5 and m = 6 is a possible solution.

Now if we use m = 6 in the other equation:

15*m = 17*k + 3

we can see if k is also an integer:

k = (15*m - 3)/17

replacing m by 6:

k = (15*6 - 3)/17 = 5.1

This solution does not work.

Let's find others:

if j = 20  (at this point we already know that the possible values of j "jump" by 15 units, like 5 + 15 = 20) then:

m = (16*20 + 10)/15 = 22

Then:

j = 20 and  m = 22 is another solution.

Same as before, let's use m = 22 in the equation for k:

k = (15*22 - 3)/17 = 19.2

Let's find another solution for m.

if  j = 35

m = (16*35 + 10)/15 = 38

Using this value of m in the k equation we get:

k = (15*35 - 3)/17 = 33.4

Let's find another solution for m.

if we take j = 50 we get:

m = (15*50 + 10)/15 = 54

Using this in the k equation we get:

k = (15*54 - 3)/17 = 47.5

Eventually, for j = 5  + 15*16 = 245 we get:  (arrived by iteration, just try each time using the previous value of j plus 15)

m = (16*245 + 10)/15 = 262

replacing this in the k equation we can find:

k = (15*262 - 3)/17 = 231.

So the first solution is:

j = 245, m = 262, k = 231

Then:

N = 262*15 = 3,930

The least number of coins that could have been stolen is 3,930.


Related Questions

Which answers describe the shape below

Answers

Answer:

B. parallelogram

Step-by-step explanation:

stay safe, stay healthy and blessed.

thank u

Answer:

a b c d e

Step-by-step explanation:

Write the equation of the linear relationship in slope-intercept form.

Answers

Answer:

y = 1/3x + 70/3

Step-by-step explanation:

2 points on the graph:

(20, 30) and (50, 40)

Slope:

m=(y2-y1)/(x2-x1)

m=(40 - 30)/(50 - 20)

m= 10/30

m= 1/3

Slope-intercept:

y - y1 = m(x - x1)

y - 30 = 1/3(x - 20)

y - 30 = 1/3x - 20/3

y = 1/3x + 70/3

if you found any words about mathematics, tell me please

Answers

Answer:

geometry

Step-by-step explanation:

left side of paper

f(x) = –?
+ x
Find f(-1)

Answers

Answer:

Replace the variable x with −1

in the expression.

f(−1)=−(−1)²−1

Simplify −(−1)²−1.

Remove parentheses.

−(−1)²−1

Multiply −1 by (−1)²

by adding the exponents.

(−1)³−1

Raise −1 to the power of 3.

−1−1

Subtract 1 from −1.

−2

Step-by-step explanation:

Hope it's right

Blueberry pies sold each day

Least:
Greatest:
Median (02):
Lower Quartile (Q1):
Upper Quartile (03):


Answers

Least: 1
Greatest:8
Median(02):4
Lower quartile(q1):3
Upper quartile(03):5

Blueberry pies sold each day So, Least: 1, Greatest:8, Median(02):4,

Lower quartile(q1):3, Upper quartile(03):5.

What are quartiles?

When we get data that can be compared relatively with each other, for finding quartiles, we arrange them in ascending or descending order.

Quartiles are then selected as 3 points such that they create four groups in the data, each group approximately possessing 25% of the data.

The lower quartile, also called the first quartile has approx 25% in its left partition, and on its right lies approx 75% of the data.

Left to right is said in the assumption that data were arranged increasingly from left to right.

From the given data

The Least number is  1.

The greatest number is 8.

The Median(02) is  4.

Lower Quartile (Q1): 3

Upper Quartile (03): 5

Learn more about quartiles here:

brainly.com/question/9260741

#SPJ2

Can you find the slope-intercept equation of each line and type the correct code? Please remember to type in ALL CAPS with no spaces.

Answers

Answer:

DIBF

Step-by-step explanation:

I'm pretty sure it's that

Sara
has
what
you can work out
she needs.
Saved & 75. This is 30% of
She needs. Explain how​

Answers

Answer:

The question seems incomplete.

Step-by-step explanation:

Sandi randomly selects a single bill from an envelope containing 8 ones, 5 fives, 4 tens, and 3 twenties. What is the expected value of the money she selects

Answers

Answer:

The expected value of the money she selects is 6.65.

Step-by-step explanation:

Expected value:

Sum of each outcome multiplied by its probability.

We have:

8 + 5 + 4 + 3 = 20 total bills.

8 are ones, so P(X = 1) = 8/20 = 0.4.

5 are fives, so P(X = 5) = 5/20 = 0.25.

4 are tens, so P(X = 10) = 4/20 = 0.2

3 are twenties, so P(X = 20) = 3/20 = 0.15.

What is the expected value of the money she selects?

[tex]E(X) = 0.4*1 + 0.25*5 + 0.2*10 + 0.15*20 = 6.65[/tex]

The expected value of the money she selects is 6.65.

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Five friends take a maths test
Adam, Brandon, Chen together scored 200 marks
Brandon, Chen and Damion together scored 215
Chen, Damion, Erica together scored 224
Damion and Erica scored more than Chen
The five of them together scored 350 marks

What are their individual scores?

Answers

Answer:

Adam scored 60, Brandon scored 66, Chen scored 74, Damion scored 75, and Erica scored 75.

Step-by-step explanation:

Since five friends took the maths test, and Adam, Brandon, and Chen together together scored 200 marks; Brandon, Chen and Damion together scored 215; Chen, Damion and Erica together scored 224; and Damion and Erica scored more than Chen; While the five of them together scored 350 marks, to determine what are their individual scores the following calculations must be done:

Adam + Brandon + Chen = 200

Damion + Erica = 150

Brandon + Chen + Damion = 215

Adam + Erica = 135

Chen + Damion + Erica = 224

Adam + Brandon = 126

Adam + Brandon = 126 + Chen = 200

Chen = 200 - 126

Chen = 74

Damion and Erica scored more than Chen

Chen + Damion + Erica = 224

74 + Damion + Erica = 224

Damion + Erica = 150

Damion = 75

Erica = 75

Brandon + Chen + Damion = 215

Brandon + 74 + 75 = 215

Brandon = 215 - 74 - 75

Brandon = 66

Adam = 350 - 75 - 75 - 74 - 66

Adam = 60

Therefore, Adam scored 60, Brandon scored 66, Chen scored 74, Damion scored 75, and Erica scored 75.

I need help doing my homework ​

Answers

Answer:

A= πr^2

45=πr^2

45/1 =22/7×r^2

45/1=22r^2/7 cross multiply

22r^2 ×1=45×7

22r^2=315 divide both sides by 22

22r^2/22=315/22

r^2=14.318

The equation $x + {y = 2 can be rewritten in a form that reveals the y-intercept of the graph of the equatior
Drag numbers to complete the equation that is equivalent to $x + žy = 2 and show the value of the y-intercept

Answers

Answer:

[tex]y = \frac{2}{z} - \frac{x}{z}[/tex]

Step-by-step explanation:

Given

[tex]x + zy = 2[/tex]

Required

Rewrite to show y-intercept

We have: [tex]x + zy = 2[/tex]

Subtract x from both sides

[tex]zy = 2-x[/tex]

Divide both sides by z

[tex]y = \frac{2}{z} - \frac{x}{z}[/tex]

The y intercet is: [tex]\frac{2}{z}[/tex]

Help plz:)))I’ll mark u Brainliest

Answers

Answer:

[tex]sin^{-1}(\frac{51}{53})\\=74.21\\[/tex]

≈74

(-2,-3) (-1,2) write the equation in y=mx+b​

Answers

Answer:

y = 5x + 7

Step-by-step explanation:

(-2, -3) & (-1, 2)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(2 - (-3)) / (-1 - (-2))

Simplify the parentheses.

= (2 + 3) / (-1 + 2)

= (5) / (1)

Simplify the fraction.

5/1

= 5

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 5x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (-1, 2). Plug in the x and y values into the x and y of the standard equation.

2 = 5(-1) + b

To find b, multiply the slope and the input of x(-1)

2 = -5 + b

Now, add 5 to both sides to isolate b.

7 = b

Plug this into your standard equation.

y = 5x + 7

This is your equation.

Check this by plugging in the other point you have not checked yet (-2, -3).

y = 5x + 7

-3 = 5(-2) + 7

-3 = -10 + 7

-3 = -3

Your equation is correct.

Hope this helps!

0.009 divided by 0.001

Answers

Answer:

9

Step-by-step explanation:

0.001 · 9 = 0.009

It’s 9 the answer is 9

Can any one psay what is monmon meaning I think it's and alien ​

Answers

Answer:

Monmon is a Beast Digimon. It is a Digimon that has the appearance of an infant monkey. It has enough strength to wield a slingshot the size of its body with ease, and confidence in its abilities to prevent its prey from escaping. It often falls from treetops due to its careless personality. Its stylish traits are its tiger-printed outfit and its white-tipped tail

In which of the following situations should the t distribution be used? a. When the sample standard deviation is used to estimate the population standard deviation b. Only when the population mean is 0 c. When the sample size is less than 30 d. When the population is not normally distributed

Answers

Answer:

a. When the sample standard deviation is used to estimate the population standard deviation

Step-by-step explanation:

T or Z distribution:

If we have the standard deviation for the sample, we use the t-distribution.

If we have the standard deviation for the population, we use the z-distribution.

Thus, the correct answer for this question is given by option a.

What is the value of P

Answers

Answer:

Hello! answer: 42

Step-by-step explanation:

These are vertical angles meaning it will have the same measure so p = 42 hope that helps!

find the radius of a circle
if the circumference is 66cm​

Answers

Answer:

10.5

Step-by-step explanation:

Multiply 0.06 by 0.021​

Answers

Answer:

Just multiply:

= 0.06×0.021

= 1.26

is this the right answer I don't even know my answer

Answer:

0.00126

Step-by-step explanation:

If you just ignore the decimals for a second, and focus on the numbers, then when you multiply 6 by 21, you get 126.0. Then move the decimal over 5 spaces, because there are 5 decimal spaces in total. Sorry if my explanation is a little confusing.

Hope that this helps!

I neeeddddd help on this I’m failing

Answers

Answer:

AB = 9

Step-by-step explanation:

Here is a simple case of a proportion.

We see that:

3:4

x:12

what can we do to make 4 into 12?

we multiply it by 3

so we do the same to 3

3*3=9

Frankie scores a 70% on her math test. The test had 20 questions. How many questions did she get correct?​

Answers

Answer:

14 questions correct

Step-by-step explanation:

x/20 *100 = 70

so x/ 20 = 70/100(0.7)

x/20 = 0.7

x = 0.7*20

x =14

14 questions correct

. The volume of a box is 405 cubic units. The length is x units, the width 4 units greater than the length, and the height is 9 units. Find the length and width of the box.

Answers

Answer:

length = 5

width = 9

Step-by-step explanation:

V = lwh

let 'x' = length

let '4+x' = width

9 = height

405 = 9x(4+x)

405 = 36x + 9x²

this is a quadratic equation:  9x² + 36x - 405 = 0

factor out a 9 to get:

9(x² + 4x - 45) = 0

9(x-5)(x+9) = 0

one root is 5 and the other is -9

since distance cannot be negative we use 5 as the length and 9 is the width

Any help would be greatly appreciated!

Answers

Answer:

the answer for that question is sqrt(49)

help needed with math​

Answers

Answer:

angle y = 49°

Step-by-step explanation:

If AB = AD and BC = DC, then the two triangles are isosceles triangles. The altitude from the top to the base divides the top angle into two equal angles, with 90° angles at the base. If angle C is divided into two equal angles (41°) and at the base is a 90° angle, that makes angle CBD 49°. On an isosceles triangle, the two angles opposite to the equal sides are identical. So angle y is identical to angle CBD.

Y=49 degree angle! Because I when you do the math you get that

1. How much salt and baking powder together is needed to make 36 cup cakes?

Answers

Answer:

too much salt will not bring taste to the cup cakes

Step-by-step explanation:

A dozen apples costs $2.35. At this rate, how much would 5 apples cost?

Answers

Answer:

0.95 is your answer

Step-by-step explanation:

Answer:

$.98

Step-by-step explanation:

so if a dozen apples cost $2.35 that can be represented by the equation 12x=2.35

so solve that for x because that is the price of a single apple

so then if you just leave it because it is a weird decimal then x times 5(to figure out how much 5 apples cost) is

(2.35/12) * 5 = 47/48 or about $.98

so five apples cost $.98

What's the answer to this? I thought it was -138 apparently it's not? :(

Answers

The answer is 78 because if you substitute with the x=3 it changes the outcome of the answer:)

Find the value of x that makes m || n

Answers

Answer:

x = 23

Step-by-step explanation:

7x - 11 = 4x + 58

(7x - 4x) - 11 = (4x - 4x) + 58

3x - 11 = 58

3x (- 11 + 11) = 58 + 11

3x = 69

3x/3 = 69/3

x = 23

2. Suppose over several years of offering AP Statistics, a high school finds that final exam scores are normally distributed with a mean of 78 and a standard deviation of 6. A. What are the mean, standard deviation, and shape of the distribution of x-bar for n

Answers

Answer:

By the Central Limit Theorem, the mean is 78, the standard deviation is [tex]s = \frac{6}{\sqrt{n}}[/tex] and the shape is approximately normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 78 and a standard deviation of 6

This means that [tex]\mu = 78, \sigma = 6[/tex]

Samples of n:

This means that the standard deviation is:

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{n}}[/tex]

What are the mean, standard deviation, and shape of the distribution of x-bar for n?

By the Central Limit Theorem, the mean is 78, the standard deviation is [tex]s = \frac{6}{\sqrt{n}}[/tex] and the shape is approximately normal.

⦁ A $10,000 certificate of deposit earns simple interest of 8 percent per year. Calculate the total earned money over the 5 year period?

Answers

Answer:

The total earned money over the 5 year period=$14,000

Step-by-step explanation:

We are given that

Principle amount, P=$10000

Rate of interest, r=8%

Time, t=5 years

We have to find the total earned money over the 5 year period.

We know that

Simple interest=[tex]\frac{P\times r\times t}{100}[/tex]

Using the formula

S.I=[tex]\frac{10000\times 8\times 5}{100}{/tex]

S.I=$4000

Now,

Amount=P+S.I

Amount=10000+4000

Amount=$14000

Hence, the total earned money over the 5 year period=$14000

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