One day last summer, Tommy decided to take a drive into the countryside.

After a few hours' drive he arrived at a farm stand. Tommy was so excited by the sight of all those fresh fruits and veggies, that he tripped getting out of his MG and knocked over a huge basket of eggs. And of course they all broke!

He asked the farmer how many eggs were in the basket because he obviously wanted to compensate her for them. She said she didn't know exactly.

"But I do know,' she said, "that this morning I decided the eggs would be easier to sell if they weren't in a big basket but if they were in little paper bags.

"So when I took all my eggs and placed two in each bag I had one left over. I didn't like that so I took the eggs and I put three in each bag. And when I did that, I also had one left over.
"When I put four in each bag, I had one left over. When I put five in a bag or six in a bag, I had one left over. And when I put seven in a bag, I had none left over."


So here's the question: what's the smallest number of eggs that Tommy should have to pay for?

Answers

Answer 1

9514 1404 393

Answer:

  301

Step-by-step explanation:

In order for the remainder to be 1 when the number is divided by 2, 3, 4, 5, or 6, it must be 1 more than a common multiple of those numbers. The least common multiple is ...

  3·4·5 = 60

So, we want a number that is 1 more than a multiple of 60 and is divisible by 7. This gives us the Diophantine equation ...

  7m -60n = 1 . . . . . where m and n are integers

Perhaps the easiest way to solve this is to try values of n between 0 and 6. We find that n=5 and m=43 will be the smallest positive value of m that satisfies this equation. This makes the number of eggs be 7×43 = 301.

Tommy should have to pay for 301 eggs.


Related Questions

Find the absolute maximum of (x^2-1)^3 in the interval [-1,2]

Answers

Let f(x) = (x ² - 1)³. Find the critical points of f in the interval [-1, 2]:

f '(x) = 3 (x ² - 1)² (2x) = 6x (x ² - 1)² = 0

6x = 0   or   (x ² - 1)² = 0

x = 0   or   x ² = 1

x = 0   or   x = 1   or   x = -1

Check the value of f at each of these critical points, as well as the endpoints of the given domain:

f (-1) = 0

f (0) = -1

f (1) = 0

f (2) = 27

So max{f(x) | -1 ≤ x ≤ 2} = 27.

solve the rational equation 8-6/x=5+12/x

Answers

I’m not really a math person but I got
x=6

x=6 is the answer to 8-6/x=5+12/x

What’s the answer please help me no links at all if you do I will report

Answers

Answer: 78

Step-by-step explanation:

1 pts
So
Sales
SE
According to
the data given, sza
what is the
sales amount
when the
temperature is
18 degrees C?
Temperature

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Shfhdjdjsxjzkzndmdkxmdns

Plzzz guys help me ;( F(x)-mx+ b, f(-2)=3 and f(4)=1 , what is the value of m and b

Answers

Answer:

Plzzz guys help me ;( F(x)-mx+ b, f(-2)=3 and f(4)=1 , what is the value of m and

least common denominator for these two rational expressions, 3/y and
1/7y

Answers

Answer:

least common denominator = 7y

Step-by-step explanation:

3/y = 21/7y

1/7y and 21/7y have a least common denominator of 7y.

-12.3 + 7v = 10.1 solve for V

Answers

Answer:

v=3.2

Step-by-step explanation:

Let's solve your equation step-by-step.

−12.3+7v=10.1

Step 1: Simplify both sides of the equation.

7v−12.3=10.1

Step 2: Add 12.3 to both sides.

7v−12.3+12.3=10.1+12.3

7v=22.4

Step 3: Divide both sides by 7.

7v /7 = 22.4 /7

v=3.2

brainliest?

If the logarithm of 5832 is 6, what is the base?
[tex] logx(5832) = 6[/tex]

Answers

Answer:

The base is 4.2426.

Step-by-step explanation:

Logarithm definition:

Suppose we have that:

[tex]\log_{a}{b} = c[/tex]

It means that;

[tex]b = a^c[/tex]

In this question:

[tex]\log_{x}{(5832)} = 6[/tex]

It means that:

[tex]x^6 = 5832[/tex]

[tex]x = \sqrt[6]{5832}[/tex]

[tex]x = (5832)^{\frac{1}{6}}[/tex]

[tex]x = 4.2626[/tex]

The base is 4.2426.

Each interior angle of a regular nonagon has a measure 13x+10°. What is x?

Answers

Answer:

Step-by-step explanation:

A nonagon has nine sides.

The sum of exterior angles = 360°, so each exterior angle is 360°/9 = 40°.

Each interior angle = 180°-exterior angle = 140°.

13x + 10° = 140°

x = 10°

PLEASE HELP !! ILL GIVE BRAINLIEST !! 100 POINTS

Answers

Answer:

third option

Step-by-step explanation:

You spin a spinner that is equally divided into 7 parts, and then you spin it again. 1 part is red, 2 parts are white, 3 parts are yellow and 1 part is black.
What is the probability of the spinner stopping on a white section on the first spin and then a red section on the second spin?

Answers

Answer:

[tex] \frac{2}{7} \: and \: \frac{1}{7} [/tex]


helppppppppppppppppppppppppp

Answers

Your answer is 40mm

3+12+12+13
=40

Answer:

The perimeter of this figure is 40 milimeters.

Step-by-step explanation:

Add all sides' lengths:

3+ 12 + 12+ 13 = 40

What is 6^4written in expanded form?
4+4+4+4+4+4
4.4.4.4.4.4
6+6+6+6
6.6.6.6

Answers

Answer:

6 · 6 · 6 · 6

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

This is because the 4 is an exponent or a power.

This makes the 6 in this case multiply itself 4 times.

HOPE THIS HELPS

Anyone know this? Answer for cookie!

Answers

Answer:

no solution

Step-by-step explanation:

the value of 3x+2y can't be two different things at once

Answer: no solutions

Step-by-step explanation:

when the two equations have the same x and y values but a different y intercept they can not have any solutions because they are parallel

Identify each pair of angles as corresponding, alternate interior, alternate exterior, or a consecutive interior and solve for X

Answers

Answer:

those are corresponding angles

Step-by-step explanation:

6x=5x+10

-5x on both sides of the equal sign

x=10

What is the product of (6a + 7) (5a – 4)?

Answers

Answer:

30a²+11a−28

Step-by-step explanation:

(6a+7)(5a−4)

=(6a+7)(5a+−4)

=(6a)(5a) + (6a)(−4) + (7)(5a) + (7)(−4)

=30a² − 24a + 35a − 28

=30a² + 11a − 28

Hope I helped! (p.s. maybe brainliest answer)

This is ur answer in the picture below

Create an inequality to describe the possible values for the total area, A, in square feet of your green section.

Answers

The Area of triangle represented using inequality is A ≤  48.67 [tex]ft^{2}[/tex].

What is Area of triangle?

The area of a triangle is half the product of its base and height.

i.e., Area of triangle= [tex]\frac{1}{2} * b* h[/tex]

Given, b= 6.2 feet and h= 15.7 feet

Area of triangle= [tex]\frac{1}{2} * b* h[/tex]

                          = 0.5 x 6.2 x 15.7

                          = 48.67 [tex]ft^{2}[/tex]

The inequality will be: Area of triangle, A≤  48.67 [tex]ft^{2}[/tex]

learn more about Area of triangle here:

https://brainly.com/question/19305981?

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It takes Bethany 9 hours to proof a chapter of Hawkes Learning Systems' College Algebra book and it takes Nina 5 hours. How long would it take them working together

Answers

Hello!

Here we could use something called the work equation.

If [tex]x[/tex] is considered proofing a chapter of the book, we can set up an equation such as, [tex]\frac{1}{9}+\frac{1}{5}=\frac{1}{x}[/tex].

Then, all we do is solve for it.

[tex]\frac{1}{9}+\frac{1}{5}=\frac{1}{x}[/tex]

[tex]5x+9x=45[/tex]

[tex]14x=45[/tex]

[tex]x=\frac{45}{14}[/tex]

So working together, it would take them [tex]\frac{45}{14}[/tex] hours to proof a chapter of the book.

Hope this helps!

Look at the picture, for the problem ​

Answers

Step-by-step explanation:

frist ordering the data

4,4,4,5,6,7,7,7,10,11 then

3. the most common ages are 4& 7

4. the range = high - low so 11 - 4 =7

5.the median is Nth/2 + Nth/2 +1 then

10th/2 +10th/2 +1

(5th +6th)/2 = median

(6 +7)/2 =13/2 = 6.5 is the median of children

Your round-trip drive to work is 4 1. miles. How many miles do you drive to and from
work in 3 days?
7 3/10
12 3/10
12 9/10
8 3/5

Answers

last one okay bye have a nice day

6 dividido entre 3,978

Answers

Answer:

0.0015082956 es la respuesta pero el valor aproximado sería ≈ 0.0015083

THE QUESTION IS IN THE PHOTO. HELP​

Answers

Answer:

The constant is 3

Step-by-step explanation:

To the answer, you divide y/x.

15/5 = 3

9/3 = 3

6/2 = 3

1.5/ 0.5 = 3

Which is a better deal on a $345 item: 40% off original price or 30% off and additional 15% at the register?​

Answers

Answer:

345 - 40% = 207$

Step-by-step explanation:

(345 - 30%) - 15% = 205.3 (Better deal)

Answer:

30% off and additional 15% at the register

Step-by-step explanation:

Deal 1

$345 × 40% = $138

$345 - $138 = $207

Deal 2

$205.30

Which of the following equations could be solved to determine the length of QR?

Answers

Answer: D

Step-by-step explanation:

Line m passes through the points (-4.3) and (4.7). What is the slope of the line that is parallel to line m?

Answers

Step-by-step explanation:

slope equals to change in y/change in x

slope=7-3/4+4

=4/8=1/2

Can someone help me? Becks?

Answers

Answer:

Perimeter = 72

Step-by-step explanation:

Notice that the adjacent (next to) lengths by each corner are equal in length.

This occurs when the quadrilateral is circumscribed.

Since 4.2 is adjacent to the length which makes up the total side 20.

20 – 4.2 = 15.8.

And 15.8 + 4.2 = 20.

(7 + 9) + (9 + 4.2) + (4.2 + 15.8) + (15.8 + 7) =

(16) + (13.2) + (20) + (22.8) =

(16 + 20) + (13.2 + 22.8) =

36 + 36 =

72

Are these 4 questions correct? If anything is wrong, let me know and tell me what is correct.

Answers

Answer:

they're all correct

Step-by-step explanation:

I think, if it's wrong I'm very sorry, but I'm fairly sure they're right

hope this helps:)

HELP ASAP NO LINKS PLEASE HELP​

Answers

the answer is D !!!!!!

A Playstation 5 gaming console is initially priced at $500 and the prices rises such that the new price is $550. What is the percent increase of the Playstation 5? Show all work, write answer using proper units.

Answers

Answer:

10%

Step-by-step explanation:

Percentage increases is given by the formula:

[tex]percentage \: increases = \frac{increases}{original \: value} [/tex]

Increases = $550 - $500 = $50

Original Value: $500

substitute the values into the formula

[tex]percentage \: increases = \frac{50}{500} \times 100[/tex]

= 10%

need help with math its a struggle

Answers

Answer:

(1,4)

(0,0)

Step-by-step explanation:

smarts

Answer:

1,4

0,0

Step-by-step explanation:

whatever is in the purple is valid and the closed line is inclusive so anything on it counts but the dotted line is exclusive

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