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

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Question 752011: A number is 1 more than twice another. Their squares differ by 176. What are the numbers?
Answer by tommyt3rd(577)

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We'll call them x and y

y=2x%2B1

then

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 3x%5E2%2B4x%2B177+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

The discriminant -2108 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -2108 is + or - sqrt%28+2108%29+=+45.912961132996

.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B4%2Ax%2B177+%29

so we see that no pair of real numbers wtii work but

%0D%0A%281%2F3%29%2A%28-2+%2B-+i+%2Asqrt%28527%29%29%0D%0A

does work

:)

Question 751847: if twice the quantity of x+6 is divided by negative 7, the result is 6 what would be the negative nuber
Answer by malglu(13)

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i think this is what you mean
2 * (x+6) all divided by minus 7 = 6
multuply both sides by minus 7
2(x+6) = -42
2x +12 =-42
2x = -54
divide by 2
x=-27

Question 751864: Ninety-eight is at most three times the sum of a number x and five

Answer by malglu(13)

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write 3 (x+5) is less then or equal to 98
so
3x +15 is less then o equl to 98
-15
3x is less then or equal to 83
divide by 3
x is less then or equal to 83/3

Question 751694: i'm a number that is exactly three times the greatest two-digit even number. what number am i ?
Answer by tommyt3rd(577)

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the greatest 2-digit even number is 98, so 3*98=294

Question 751648: three added to five times a number is thirteen.
3+5x=13
-3 -3
5x=10
x=2
Answer by Yanisleysi (5)

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Question 751612: One number is 4 greater than another number. When three times the smaller number is added to twice the larger one, the result in 43. Find the numbers.
What is the formula for this question?

Answer by stanbon(57357)

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One number is 4 greater than another number. When three times the smaller number is added to twice the larger one, the result in 43. Find the numbers.
---
If x = y + 5, y must be the smaller number.
3y + 2x = 43
-----
Substitute for "x" and solve for "y":
3y + 2(y+5) = 43
3y + 2y + 10 = 43
5y = 33
y = 33/6
-------
Solve for "x":
x = y + 5
x = (33/6) + (30/6)
x = 63/6
=====================
Cheers,
Stan H.
=====================

Question 751517: Campus Rentals rents 2- and 3-bedroom apartments for $700 and $900 a month respectively. Last month they had six vacant apartments and reported $4600 in lost rent. How many of each type of apartment were vacant?
Answer by dkppathak(40)

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rent of two room apartment is $700 pm and 3 room apartment is $900
total apartment remain vacant are 6
loss was $4600
let x 2 room apartment
and y 3 room apartment
x+y +6 i
700 x+900 y =4600 ii
multiply first equation by 700 we will get
700x+900 y=4200 iii
by solving eqn ii and iii
we will get x=4
and y=2
ANSWER 2 room apartment vacant are 4
3 room apartment vacant are 2

Question 751470: divide the product of 7 and 7 by 5

Answer by Cromlix(353)

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The product (7 x 7) = 49
Divide this by 5
49/5 = 9.8
Hope this helps
:-)

Question 751200: hello i tried answering this question but i need a second opinion find the number that is less than the product of 18 times the sum of 16 and 23
Answer by Edwin McCravy(8909)

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You left out something because there are many
numbers that are less than 648, which is the
 product of 18 times the sum of 16 and 23.

I think the number you left out was a number that shuld go in the
blank below:

find the number that is ___ less than the product of 18 times the 
sum of 16 and 23.

Edwin

Question 751280: one less than the product of my number and 5 is 9 what is my number
Answer by tommyt3rd(577)

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one less than (the product of my number and 5) : 5x-1
...is 9: =9

so 5x-1=9
and so x=2

Question 751224: find the number that is 2 more than 3 times 5 ?
Answer by Edwin McCravy(8909)

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Multiply 3 times 5, then make it 2 more by adding + 2 on the right of it:

            3×5 + 2

That becomes
           
             15 + 2

which becomes  

               17 

Edwin

Question 750854: Find the five digit number in which the first two digits are the square of the third, the third isdouble the second, the last two digits are the sum of the second and third, and the last is one half the second and one third the first. The sum of all the digits is 21.
Answer by Edwin McCravy(8909)

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Draw 5 blanks for the 5 digits:

the last is one half the second and one third the first

That narrows it to these three possibilities:
3 2     1

6 4     2

9 6     3

the first two digits are the square of the third

The only one of those three that has the first two digits 
forming a square is

6 4     2
since 64 is the square of 8.  So the third digit is 8.

6 4 8   2

the last two digits are the sum of the second and third

4+8=12 so the last two digits is 12, which means the
fourth digit is 1
6 4 8 1 2

That's the answer!

We didn't need to use:

the third is double the second,

But it checks since 8 is indeed double 4
We also didn't need to use

The sum of all the digits is 21.

But it checks also since 6+4+8+1+2 = 21 

Edwin

Question 750958: what algebraic equation represents "four times the sum of a number, x, and eight equals nineteen?
Found 2 solutions by tommyt3rd, stanbon:
Answer by tommyt3rd(577)   (Show Source):
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4(x+8)=19

Answer by stanbon(57357)   (Show Source):
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what algebraic equation represents "four times the sum of a number, x, and eight equals nineteen?
-----
4(x+8) = 19
======================
Cheers,
Stan H.

Question 750961: how do i write a equation the represents "six times the difference of a number, x, and fourteen equals nine"?
Answer by JoeTaxpayer(130)   (Show Source):
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6(x-14)=9

Question 750895: Find two non negative integers that have the same answer when multiplied together as when one is added by the other
Answer by Edwin McCravy(8909)   (Show Source):
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Two solutions, 1. the pair of non-negative integers 0 and 0 0×0 = 0 0+0 = 0 2. the pair of non-negative integers 2 and 2 2×2 = 4 2+2 = 4 Edwin

Question 750543: what is a expression for the verbal expression four times the product of x and y increased by the sum of y^2, xy, and 5
Answer by JoeTaxpayer(130)   (Show Source):
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Question 750274: 232 is a number written in base 5. What is it written in base 10?
Answer by Alan3354(30993)   (Show Source):
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232 is a number written in base 5. What is it written in base 10?
= 2*25 + 3*5 + 2
= 67

Question 750060: The average of two numbers is 62. If 2 is added to the smaller number, the ratio between
the numbers become 1:2. The smaller number is

Answer by sachi(392)   (Show Source):
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let the smaller number is x
The average of two numbers is 62
so the bigger no is 2*62-x=124-x
2 is added to the smaller number, the ratio between the numbers become 1:2
x+2:124-x=1:2
or 2(x+2)=124-x
or 2x+4=124-x
or 3x=120
or x=40

Question 750130: solve for equation for; four teimes the sum of a number and three is equal to eight more than twice the same number?
Found 2 solutions by sachi, stanbon:
Answer by sachi(392)   (Show Source):
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let the no is x
four times the sum of a number and three is equal to eight more than twice the same number
so 4(x+3)=8+2x
or 4x+12=8+2x
or 4x-2x=8-12=-4
or 2x=-4
or x=-2

Answer by stanbon(57357)   (Show Source):
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solve for equation for; four teimes the sum of a number and three is equal to eight more than twice the same number?
-------
Equation:
4(x + 3) = 2x+8
----------------------
4x + 12 = 2x + 8
------
2x = -4
x = -2
=============
Cheers,
Stan H.
=============

Question 750063: plzzz help me sir,If 7 maids with 7 mops chaned 7 floors in 7 hours, how long would it takes 3 maids to mop
3 floors with 3 mops?
Answer by Alan3354(30993)   (Show Source):
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If 7 maids with 7 mops chaned 7 floors in 7 hours, how long would it takes 3 maids to mop
3 floors with 3 mops?
------------
Maids and mops are the same.
7 floors = 7 maids * 7 hours = 49 maid-hrs
1 = 7 maid-hrs
----
3 floors = 21 maid-hrs
21 maid-hrs/3 maids = 7 hours
-----
how long would it takes 3 maids to mop 3 floors with 3 mops?
7 hours

Question 749874: when a number is divided by 4 and has 28 added to it the result is equal to twice the number.find the number.solve this quadritic word problem by making equation by factorizing.
Answer by timvanswearingen(106)   (Show Source):
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Let the number be x. Then the problem can be set up as follows:

Mutiply both sides by 4:

Subtract x from both sides:

Divide both sides by 7:

The number is 16.

Question 749889: A length of copper wire is to be cut into two pieces so that the first piece is 7 feet shorter than three times the length of the second piece. If the total length given is 29 feet, find the length of each piece.
Thank You
Answer by josmiceli(9681)   (Show Source):
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Let = the length of the 1st piece
Let = the length of the 2nd piece
given:
(1)
(2)
-----------------
(1)
(2)
Add the equations

and, since
(2)
(2)
(2)
The length of the 1st piece is 20 ft
The length of the 2nd piece is 9 ft
check:
(1)
(1)
(1)
(1)
OK

Question 749528: the sum of two numbers is 70.4 one is 9 times the other.

Answer by timvanswearingen(106)   (Show Source):
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Let the smaller number be x. Then the larger number is 9x. Since their sum is 70.4, then:

Combine like terms:

Divide both sides by 10:

The other number is 9x, so plug in 7.04 for x:

So the numbers are 7.04 and 63.36

Question 749505: the sum of three numbers is 66. the third number is 9 more than the first. the second number is 3 times the third. what are the numbers?
Answer by timvanswearingen(106)   (Show Source):
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Let x represent the third number. Then the first number is x-9 and the second number is 3x.
Now, the sum of the numbers is 66, so set up an equation:

Combine like terms:

Add 9 to both sides:

Divide both sides by 5:

Thus, the third number is 15. The second was 3x, so 3*15=45. The second number is 45. The first number was x-9, so 15-9=6. The first number is 6. The numbers are 6, 45, and 15.

Question 749500: • My tens and ones digits are both odd; my ones digit is 300% of my tens digit.
• The sum of my thousands and hundreds digits is equal to my ones digit.
• The sum of all of my digits is 21.

Answer by timvanswearingen(106)   (Show Source):
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You have two choices for the tens and ones digits, respectively.
The number will be xx13 or xx39, the sum of the first two digits is the same as the last, and the sum of all four is 21. If the sum of the first two digits was 3, the sum of all four would only be 7. If the sum of the first two digits is 9, then 9+3+9=21. Therefore the number is of the form xx39 where the first two digits add up to 9.
9039
1839
8139
2739
7239
3639
6339
4539
5439
Those would all work

Question 749441: If the product of 14 and a number is decreased by 7, and then the result is divided by 5, the answer is 7. What is the unknown number?
Answer by checkley79(3050)   (Show Source):
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(14x-7)/5=7 cross multiply
14x-7=7*5
14x-7=35
14x=35+7
14x=42
x=42/14
x=3 ans.
Proof:
(14*3-7)/5=7
(42-7)/5=7
35=7*5
35=35

Question 749286: The difference between 2 numbers is 46. 5 times the smaller is equal to 2 more than the larger. What are the numbers?
Answer by stanbon(57357)   (Show Source):
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The difference between 2 numbers is 46. 5 times the smaller is equal to 2 more than the larger. What are the numbers?
-----------
Equations:
x - y = 46
5y = x + 2
-----
Rearrange:
x = y + 46
x = 5y - 2
-----
Substitute:
y+46 = 5y-2
4y = 48
y = 12
------
Solve for "x":
x = y + 46
x = 12 + 46 = 58
-------
Cheers,
Stan H.
=============

Question 749272: I'm thinking of a number. If you multiply it by 5 and then take away 7, you will get 53. what is my number?
Answer by 932982(3)   (Show Source):
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5x(x is the number your thinking of) -7=53
5x-7=53
+7 +7
5x=60
divide both sides by 5
x= 12
you are thinking of the number 12

Question 749166: The difference between two numbers is 42. If one-half of the larger number is three more than twice the smaller number, what are the two numbers?

Answer by JoeTaxpayer(130)   (Show Source):
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L = large, S= small
L-S=42 rearrange to L=S+42
.5L=2S+3 multiply both sides for easy reading to L=4S+6
Since L=S+42 and L=4S+6 then S+42=4S+6
S+36=4S
3S=36
S=12, L=54

Question 749154: Count the total number of words in this question and multiply it by two and then subtract three
Answer by timvanswearingen(106)   (Show Source):
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18*2=36
36-3=33

Question 749147: 1035 minus what will equal 308
Answer by timvanswearingen(106)   (Show Source):
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Just take 1035 and subtract 308 to find the number. 1035-308=727
Check: 1035-727=308

Question 748992: The camera Melissa wanted for her birthday is on sale at 41% off the usual price. The amount of the discount is $155.80. What was the original price of the camera?
Answer by timvanswearingen(106)   (Show Source):
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If the discount was $155.80, then 41% of the original price is $155.80. Let p be the original price:

Divide both sides by 0.41:

The original price of the camera was $380

Question 748981: I am a 6 digit number. All my digits are teh same. The sum of all my digits after being subtracted from the largest 6 - digit number is 6. Find out who i am?
I am trying to find out, but do not have any clue. please help me out.
Regards

Answer by timvanswearingen(106)   (Show Source):
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The largest six digit number is 999,999...if all the digits in your number are the same, you will end up with six digits that are all the same again after you subtract from 999,999. Since the sum of the digits after subtracting is 6, and you have 6 digits, then each digit is a 1 and the difference of 999,999 and the number you are looking for is 111,111.
So what number would you subtract from 999,999 to get 111,111?
I bet you see it now, it's 888,888

Question 748822: In two digit number,the product of its digits is 18.if the places of the digits are interchanged,the number so formed is greater than the original number by 27,find the original number.
Answer by stanbon(57357)   (Show Source):
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In two digit number,the product of its digits is 18.if the places of the digits are interchanged,the number so formed is greater than the original number by 27,find the original number.
----
Let the number be 10t+u
----
Equations:
t*u = 18
10u+t - (10t+u) = 27
-----
Simplify:
t*u = 18
9u - 9t = 27
-----
t*u = 18
u - t = 3
----
t*u = 18
u = t+3
-----
t(t+3) = 18
t^2 + 3t -18 = 0
(t-6)(t+3) = 0
Positive solution:
t = 6
=====
solve for "u":
u = t + 3
u = 9
-------
Ans: 10t+u = 10*6+9 = 69
===============================
Cheers,
Stan H.

Question 748694: the sum of two numbers is 81 the differance of the same two numbers is 9. What are the two numbers?
Answer by Cromlix(353)   (Show Source):
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x + y = 81
x - y = 9
Add
2x = 90
x = 45
Substitute x = 45
in first equation
45 + y = 81
y = 81 - 45
y = 36
{45,36}

Question 748662: the quotient of 18 and x is equal to 6
Answer by stanbon(57357)   (Show Source):
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the quotient of 18 and x is equal to 6
----------
18/x = 6
---
18 = 6x
x = 18/6
x = 3
-------------
Cheers,
Stan H.
=============

Question 748623: What is the sum of 53 and 8?
Answer by Cromlix(353)   (Show Source):
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The sum of 53 and 8
is 61.

Question 748637: its greater than 100 less than 200 its prime and the sum of its digits is 13
Found 2 solutions by timvanswearingen, tommyt3rd:
Answer by timvanswearingen(106)   (Show Source):
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157
You can narrow it down a little. You know the first digit is a 1, the last digit has to be odd for it to be prime, but can't be 1 since the sum of the digits is 13, and the middle digit has to also be odd for the sum of the digits to be 13.

Answer by tommyt3rd(577)   (Show Source):
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From a list of primes between 100 and 200 we get these choices:

139, 157, 193

:)

Question 748474: The sum of two positive integers is 51. The first number is twice the second number. Find the two numbers.
Answer by tommyt3rd(577)   (Show Source):
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n+m=51
m=2n

n+2n=51
3n=51
n=51/3
n=17
so the two numbers are 17 and 34

:)

Question 748374: a number is tripled and added to 9. The result is six times the number itself.
is it something like n(3)+9=n^6

or n^3 i dont know...
Answer by JoeTaxpayer(130)   (Show Source):
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Tripled means multiplied by 3. X^3 is read X cubed and is X * X * X.
So 3X+9= 6X
9=3X
X=3

Question 748132: it is a 9 digit number.
the pattern is odd,even,odd.......odd.i.e. starting and ending with an odd digit.
this is divisible by 9 now and when we start removing 1 digit from right step by step..
the number left after every step is divisible by the total number of digits .
hint-the 5th digit is 5 only and no digit shall repeat digits from 1-9 should be there.

Answer by solver91311(16897)   (Show Source):
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381654729

Question 748156: The sum of three numbers is 60. The second is five less than the first, the third is half the second, what are the numbers?
Answer by kibauu(29)   (Show Source):
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A+B+C=60
B=A-5 --> A=B+5 ....(1)
C=1/2B ....(2)
A+B+C=60 = (B+5)+B+(1/2B)=60
2B+1/2B=55
5/2B=55
B=55x2/5=22
As B is 22, so A is B+5=27
C=22x1/2=11
so they are 27,22,11