1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
pochemuha
1 year ago
15

if the eggs in a basket are removed 2 at a time, 1 egg will remain. if the eggs are removed 3 at a time, 2 eggs will remain. if

the eggs are removed 4, 5, or 6 at a time, then 3, 4, and 5 eggs will remain, respectfully. but if they are taken out 7 at a time, no eggs will be left over. find the least number of eggs that could be in the basket.
Mathematics
1 answer:
Yanka [14]1 year ago
4 0

The least number of eggs that could be in the basket is 119.

Multiple of the number:

The multiple is the numbers you get when you multiply a certain number by an integer.

Given,

If the eggs in a basket are removed 2 at a time, 1 egg will remain.

If the eggs are removed 3 at a time, 2 eggs will remain.

If the eggs are removed 4, 5, or 6 at a time, then 3, 4, and 5 eggs will remain, respectfully.

But if they are taken out 7 at a time, no eggs will be left over.

Here we need to find the least number of eggs in the basket.

Let the number of eggs in the basket be N.

We know that,

if the eggs in a basket are removed 2 at a time, one eggs will remain.

So N is 1 less than a multiple of 2, so

=> N=2A-1

If they are removed 3 at a time, 2 eggs remain.

So N is 2 more, and therefore 1 less than, a multiple of 3, so

=> N=3B-1

If the eggs are removed 4...at a time, then 3...eggs remain,

So N is 3 more, and therefore 1 less than, a multiple of 4, so

=> N=4C-1

Similarly,

For 5,

=> N = 5D - 1

For 6,

=> N = 6E - 1

So,  if they are taken out 7 at a time, no eggs will be left over.

So,

N => 7F

Where A,B,C,D,E, and F are any positive integer.

Therefore,

N = 2A-1 = 3B-1 = 4C-1 = 5D-1 = 6E-1 = 7F

Add 1 to all those:

N+1 = 2A = 3B = 4C = 5D = 6E = 7F+1

Through this,

N + 1 = 7F + 1

has to be a common multiple of 2,3,4,5,6.

So, the LCM of 2,3,4,5,6 is 60.

So N+1 is a multiple of 60 which means N is 1 less than a multiple of 60.

So we find the least multiple of 60 that is 1 more than a multiple

of 60.

The multiples are, 60, 59, ....but 59 is not a multiple of 7.

The next multiple of 60 is 120.  

1 less than 120 is 119, and sure enough, 119 is a multiple of 7.

So,

=> 119 = 17*7.

Therefore, the least number of eggs that could be in the basket is 119.

To know more about Multiple here

brainly.com/question/5992872

#SPJ4

You might be interested in
IOr — 5г + 3r — 8г i need help
Anni [7]

Answer:

0r

Step-by-step explanation:

Since they all have r you can pretend it s not there and add it on at the end.

Now 10 - 5 is 5. 5 + 3 is 8. 8 - 8 is 0. tack the r onto the end and you get 0r.

3 0
2 years ago
Evaluate.<br><br> 4^3−4÷2⋅5<br><br><br> 20<br><br> 40<br><br> 54<br><br> 150
nika2105 [10]

Answer:

150

Step-by-step explanation:

1. 4^3 = 4 x 4 x 4 = 16 x 4 = 64

2. 64 - 4 = 60

3. 60 ÷ 2 = 30

4. 30 ⋅ 5 = 150

3 0
2 years ago
The teacher has 15 gold prize ribbons, 22 blue ribbons, and 5e red ribbons. There are 12 boys and 18 girls in the class. If the
natulia [17]

Answer:

3

Step-by-step explanation:

Given

15 gold ribbons

22 blue ribbons

53 red ribbons

Total of 53 + 22 + 15 = 90 ribbons

Total number of students = 12 boys + 18 girls = 30 students.

If evenly divided, each student will have 90/30 = 3 ribbons

The expression to solve would basically be the amalgamation of what we did above:

(53 + 22 + 15)/(12+18)

4 0
3 years ago
If the sum of all interior angles of a regular polygon is 1080 degrees then number of sides of the polygon is?
MakcuM [25]

Answer:  8

<u>Step-by-step explanation:</u>

The formula for the sum of the angles of a polynomial is:

S_n=180(n-2)

1080 = 180(n - 2)

1080 = 180n - 360

1440 = 180n

8 = n

6 0
3 years ago
Can you help me please!!!!
pentagon [3]
If you add the 3/4s with the 2 1/4 hour breaks it would be 1 hour and 1 fourth.
Then you take 10-1/2 hours and subtract it by 1 hour and 1 fourth.
So you would get 9-1/4 hours
5 0
3 years ago
Read 2 more answers
Other questions:
  • Which expression has the least value when x=100 <br><br> a. 1/x<br> b. 10/x<br> c. 1-x<br> d. 10-x
    10·2 answers
  • 1. A total of 498 tickets were sold for the school play. They were either adult tickets or student tickets. There were 53
    13·1 answer
  • Katrina is building a deck. She cuts 3 lengths of wood from a 72-inch board. The first length is inches. The second length is in
    12·2 answers
  • Determine the following angle measures.<br> mZM=<br> mXL =
    14·1 answer
  • Is 1/2 and 1/8 equivalent fractions
    8·2 answers
  • How are the values of the eights in 880 related
    6·1 answer
  • Correctly complete this sequence: 88511, 16351, ?, 10251
    10·1 answer
  • Please help me find X.
    8·2 answers
  • An Internet company reported that its earnings will be less than the 24 cents per share that was predicted. Write an inequality
    6·2 answers
  • What is the sum of 4 and its addictive inverse
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!