Questions on Word Problems: Numbers, consecutive odd/even, digits answered by real tutors!

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What is the shortest piece of rope i would be able to divide into lengths of 4m ,6m and 9m without having to throw away any of the rope? Also state how many pieces of each length there must be.
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36 meters
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36/4 = 9 pieces, etc.

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I think it's m
pieces of 4 m lengths
pieces of 6 m lengths
pieces of 9 m lengths
I noticed that won't work since

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F=first number S=second number

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Person who answed this must have missread secound part, it says it equals one and a half, not one half. The correct answer is 9/10 using the same logic.

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>>...when you divide the number by 9 there are 4 left over...<<

That says the number has to be 4 more than a multiple of 9

The multiples of 9 are

{9,18,27,36,45,54,63,72,81,90,...}

The numbers which are 4 more than a multiple of 9 are

Possible answers: {13,22,31,40,49,58,67,76,85,94,...}

So the number must be one of those.

>>...when you divide the number by 8 there are 2 left over...<<

That says the number has to be 2 more than a multiple of 8

The multiples of 8 are

{8,16,24,32,40,48,56,64,72,80,88,96}

The numbers which are 2 more than a multiple of 8 are

Possible answers: {10,18,26,34,42,50,58,66,74,82,90,98}

So the number must be one of those.

The only number common to both sets of possible answers is 58.  However
we only took the numbers up to 100.  It may be that there would be other
numbers is common if we took higher numbers.  But let's see if 58 satisfies 
the other requirement. If not we'll have to get more elements of those
sets.

>>...when you divide the number by 5 there are 3 left over...<<

That's true of 58 because it's 3 more than 55 which is a multiple of 5.
So we didn't have to go higher to find the answer.

Answer: 58.

Edwin

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If you are asking about "another way," then there must be an example already done. What does that look like? We would be delighted to help, but you have to tell the whole story.

John

My calculator said it, I believe it, that settles it

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what is the lagest 4 digit even number you can make with the numbers 1234?
Ans: 4312

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Let
x = larger number
y = smaller number

Given
The sum of two numbers is 31
x+y=31
x=31-y..........(1)
A number is 5 less than three times another number
x=3y-5..........(2)
Put the value of x from (2) to (1)
3y-5=31-y
3y+y=31+5
4y=36
4y/y=36/4
y=9
Put the value of y in (1)
x=31-y
x=31-9
x=22
Numbers are 22 and 9

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Rational numbers are numbers that can be written as a ratio of two integers
, , , and are rational numbers.
, and are not rational numbers. They are called irrational numbers. The irrational numbers, together with the rational numbers, make up the real numbers.

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The question is I am thinking of two whole numbers. The second is larger than the first. The sum of the squares of the numbers is 61.What are the two numbers? Explain how you came up with that answer. Thanks
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61 - 1 = 60, not a perfect square
61 - 4 = 57, "
61 - 9 = 52, "
61 - 16 = 45 "
61 - 25 = 36 --> 5 & 6
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Works for small numbers

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Consider a series of odd numbers such as 1, 3, 5, 7, 9, 11 and so on. This series consists of consecutive odd numbers because no odd number is left out. Now, notice the particular feature of this series is that each number is 2 greater than the number that comes just before it. So if 5 is the first odd number you select, the next consecutive odd number is 5 + 2 or 7. And think about this. The next consecutive number after that is two more than its predecessor, so it is 7 + 2 or 9. But 7 is equal to 5 + 2. So we can say that the third number in this series of consecutive odd numbers is (5 + 2) + 2 = 5 + 4 = 9. In fact we can write the series of consecutive odd numbers starting with 5 as (5), (5 + 2), (5 + 4), (5 + 6), (5 + 8), and so on.
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In general we can similarly write the series of odd numbers in which n represents the unknown first number, as n, n+2, n+4, n+6, n+8, ...
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So three consecutive odd numbers can be written as n, n+2, and n+4. The problem asks you to find three consecutive odd numbers whose sum is 303. You can set up the equation for the sum of three consecutive odd numbers as equal to 303 by writing it as follows:
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n + (n+2) + (n+4) = 303
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You can now simplify the left side by adding the three n terms to get 3n and then adding the 2 and the 4 to get 6. This makes the equation become:
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3n + 6 = 303
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First get rid of the 6 on the left side by subtracting 6 from both sides to simplify the equation to:
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3n = 297
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Solve for n by dividing both sides of the equation by 3 (the multiplier of x) to reduce the equation to:
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n = 99
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We identified n as the first term in the series. So the second consecutive odd term must be 2 more that 99, or it must be 101. And the third consecutive odd term must be 2 more than the second term, so it must be 103.
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Check the answer by adding 99 + 101 + 103 to ensure that the sum of these three consecutive odd numbers is 303, just as the problem requires it to be.
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In summary, the 3 consecutive odd numbers that add to a total of 303 are 99, 101, and 103.
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I hope this helps you to understand how to work problems having consecutive odd numbers.
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THE DIFFERENCE between 54 tens and the largest 2 digit number is

54 tens means 54 times 10 which is 540

The largest 2 digit number is 99

So the problem asks for the difference between 540 and 99.

To find the difference between a first number and a second number,
you subtract:  first number - second number.

            540 - 99 = 441

Edwin

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THE DIFFERENCE between 54 tens and the largest 2 digit number is

54 tens means 54 times 10 which is 540

The largest 2 digit number is 99

So the problem asks for the difference between 540 and 99.

To find the difference between a first number and a second number,
you subtract:  first number - second number.

            540 - 99 = 441

Edwin

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Let represent one of the numbers.

Let represent the other.

You are given that:



and



Solve the 2X2 system by substitution.

John

My calculator said it, I believe it, that settles it