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Question 242430

Five times the difference of twice a number and eight is negative ten. Find the number.

Found 2 solutions by unlockmath, JimboP1977:

Answer by unlockmath(140)

(Show Source):

You can put this solution on YOUR website!
Hello,
These written problem can be difficult to understand. But once we get all the words and their meanings then it comes together. The word "is" usually means equal. Here's how this will look.
5(2x-8)=-10 Multiply out will give us:
10x-40=-10 Add 40 to both sides will be:
10x=30 Divide both sides by 10 will be:
x=3 Enter this into the equation and it works out.
RJ Toftness
www.math-unlock.com

Answer by JimboP1977(93)

(Show Source):

You can put this solution on YOUR website!
5(2x-8)=-10
10x-40 = -10
10x = 30
x =3

Question 242432: what does this mean: find two consecutive numbers with a product of 210?
Found 2 solutions by JimboP1977, stanbon:
Answer by JimboP1977(93)   (Show Source):
You can put this solution on YOUR website!
well consecutive means one after another or following each other.
The product of two numbers is just another way of saying two numbers multiplied together.
Does that help?
Let x = a number
let x+1 = the next number
x times by x+1 = 210

(called completing the square)

so the two numbers are 14 and 15. Check the answer by multiply both together to give 210.
Do you understand it?

Answer by stanbon(26367)   (Show Source):
You can put this solution on YOUR website!
what does this mean: find two consecutive numbers with a product of 210?
----------------------
1st number: x
2nd number: x+1
-----------------------
Equation:
x(x+1) = 210
x^2 + x - 210 = 0
(x-14)(x+15) = 0
x = 14 or x = -15
=========================
Two possible solutions:
x = 14
x+1 = 15
---
OR
---
x = -15
x+1 = -14
=================
Cheers,
stan H.

Question 242307: twice the sum of 4 and three times some number is 34. whats the number?
Answer by unlockmath(140)   (Show Source):
You can put this solution on YOUR website!
Hello,
Let's put this into the following. (Hint:In word problems the word "is" usually means equal.)
2(4+3x)=34 Multiply this out will give us:
8+6x=34 Subtract 8 from both sides will be:
6x=26 Divide 6 into both sides will be:
x = 26/6 or 4 1/3
RJ Toftness
www.math-unlock.com

Question 242261: Twice a first number plus a second number is 18. The first number is five less than three times the second number. Find the numbers. Show equations.
Answer by nyc_function(290)   (Show Source):
You can put this solution on YOUR website!
2x + y = 18
x = 3y - 5
Those are your equations.
Can you finish now?
=====================================================
I got your e-mail. Here is the entire problem solved.

Good morning. I got your reply lasy night. Here is how we do your math problem.
Twice a first number plus a second number is 18. The first number is five less than three times the second number. Find the numbers. Show equations.

Solution:

Let x = one number
let y = the other number

2x + y = 18
x = 3y - 5

I will use the substitution method, which is the easiest to follow.

Plug 3y - 5 into the other equation and solve for y.

2(3y - 5) + y = 18

6y - 10 + y = 18

7y = 18 + 10

7y = 28

y = 28/7

y = 4

Since we now know y = 4, we plug 4 for y into EITHER of the original equations created from the word problem.

I will use x = 3y - 5.

Let y = 4

x = 3(4) - 5

x = 12 - 5

x = 7

The numbers are 4 and 7.

Did you follow?

Guido

Question 242180: Denise bought 50 postage stamps for which she paid $13.00. Some were 20-cent stamps and some were 40-cent stamps. How many of each did she buy?
Answer by checkley77(7172)   (Show Source):
You can put this solution on YOUR website!
X+Y=50 OR X=50-Y
.20X+.40Y=13
.20(50-Y)+.40Y=13
10-.20Y+.40Y=13
.20Y=13-10
.20Y=3
Y=3/.20
Y=15 40 CENT STAMPS WERE BOUGHT.
50-15=35 20 CENT STAMPS WERE BOUGHT.
PROOF:
.20*35+.40*15=13
7+6=13
13=13

Question 242194: Bill has twice as much money as Bob. Paul has $12 more than Bill. Together they all have $92. How much does Bob have?
Answer by rapaljer(3631)   (Show Source):
You can put this solution on YOUR website!
Let x= Bob
2x=Bill
2x+12=Paul

x+2x+2x+12=92
5x+12= 92
5x=80
x=16 Bob
2x=32 Bill
2x+12= 44 = Paul

Check: 16+32+44=92 total

Dr. Robert J. Rapalje, Retired

Question 242183: One week a business sold 40 scarves. White ones cost $4.95, and printed ones cost $7.95. In all, total sales of scarves were $282. How many of each kind were sold?
Answer by checkley77(7172)   (Show Source):
You can put this solution on YOUR website!
P+W=40 OR P=40-W
4.95W+7.95(40-W)=282
4.95W+318-7.95W=282
-3W=282-318
-3W=-36
W=-36/3
W=12 WHITE SCARVES WERE SOLD.
40-12=28 PRINTED SCARVES WERE SOLD.
PROOF:
4.95*12+7.95*28=282
59.4+222.6=182
282=282

Question 242106: If 5 times the smaller of two numbers is subtracted from twice the larger, the result is 16. If the larger is increased by three times the smaller, the result is 63. Find the larger number.
Answer by blwinbbbles(6)   (Show Source):
You can put this solution on YOUR website!
write down what you have..use S for smaller and L for larger
you know that 5S subtracted from 2L is equal to 16
So: 2L - 5S = 16
and you know that L + 3S = 63 and you can write this so L = 63-3S
use substitution:
2(63-3S) - 5S = 16....solve for S
Once you have S then plug it into one of the equations and solve for L
Good Luck

Question 242104: The sum of two numbers is 50. If twice the larger is subtracted from four times the smaller, the result is 8. Find the numbers.
Answer by checkley77(7172)   (Show Source):
You can put this solution on YOUR website!
X+Y=50 OR X=50-Y
4X-2Y=8
4(50-Y)-2Y=8
200-4Y-2Y=8
-6Y=8-200
-6Y=-192
Y=-192/-6
Y=32 ANS.
X+32=50
X=50-32
X=18 ANS.
PROOF:
4*18-2*32=8
72-64=8
8=8

Question 242103: The difference between two numbers is 34. The larger exceeds three times the smaller by 4. What is the smaller number?
Answer by College Student(266)   (Show Source):
You can put this solution on YOUR website!
Let one number = x
The larger number is = 3x+4
Their difference is 34.
.
Here is your equation:
.
Solve for x to determine its value and plug it into (3x+4) to find the larger value. Be careful with the negative sign.
.
Remember to check your answers by pluging the x value in the original equation. Both sides must equal to each other.

Question 242101: The sum of two numbers is 104. The larger is 1 less than twice the smaller number. Find the numbers.
Answer by College Student(266)   (Show Source):
You can put this solution on YOUR website!
Let one number = x
The other number is 1 less than twice the smaller number = 2x-1
Their sum is 104.
.
Here is your equation:
.
Solve for x to determine its value and plug it into (2x-1) to find the other value.
.
Remember to check your answers by pluggin the x value in the original equation. Both sides must equal to each other.

Question 242108: the sum of three numbers is 137. the second number is four more than two times the first number. The third number is five less than three times the first number. Find the number.

Answer by College Student(266)   (Show Source):
You can put this solution on YOUR website!
Let the first number = x
Thus, the second number is = 2x+4
And, the third number is = 3x-5
Their sum is 137.
.
So, our equation then becomes:

Now solve for x to determine its value. I'll let you do the algebra.
.
Remember to check your answer by pluggin the x value in the equation. Both sides must equal to each other in order for the answer to be valid.
.
Done! :)

Question 241901: The tens digit of a given two-digit positive number is two more than three times the units digit. If the digits are reversed, the new number is 13 less than half the given number. Find the given integer.
Answer by ankor@dixie-net.com(6707)   (Show Source):
You can put this solution on YOUR website!
Let x = the tens digit
Let y = the units
then 10x+y = "the number"
:
Write an equation for each statement, just as it says:
:
"The tens digit of a given two-digit positive number is two more than three times the units digit."
x = 3y + 2
:
"If the digits are reversed, the new number is 13 less than half the given number."
10y+x = .5(10x+y) - 13
10y + x = 5x + .5y - 13
10y - .5y = 5x - x - 13
9.5y = 4x - 13
:
Find the given integer.
:
From the 1st statement, replace x with (3y+2) in the above equation:
9.5y = 4(3y+2) - 13
9.5y = 12y + 8 - 13
9.5y = 12y - 5
+5 = 12y - 9.5y
5 = 2.5y
y =
y = 2
then
x = 3(2) + 2
x = 8
:
82 is the number
:
:
Check solution in the statement:
"If the digits are reversed, the new number is 13 less than half the given number."
28 = .5(82) - 13
28 = 41 - 13

Question 241943: what two whole numbers have a product that is three times greater than their sum
Answer by edjones(3330)   (Show Source):
You can put this solution on YOUR website!
xy=3(x+y)
xy=3x+3y
-3y+xy=3x
y(x-3)=3x
y=3x/(x-3)
.
A whole number is any positive integer and zero.
Look at the graph below.
There are the only 2 answers:
0 and 0.
4 and 12
.
Ed
.

Question 241923: find the two consecutive numbers that have digit sums of 27 and 1
Answer by Alan3354(6153)   (Show Source):
You can put this solution on YOUR website!
999 and 1000. There might be others, but I don't think so.

Question 241945: There are 3consecutive integers.The sum of the first two is 35 than the third.Find the integers
Answer by College Student(266)   (Show Source):
You can put this solution on YOUR website!
Did you mean to say the sum of the first two is 35 MORE than the third? (you didn't specify the relationship between 35 and the third integer, but I'm going to assume "more").
.
Let x = integer
Let x+1 = consecutive integer
Let x+2 = the next consecutive integer
.
Our equation then becomes:

Now remove the parenthesis and workout the algebra.
The solution for x+2=38

Question 241947: There are 3 consecutive integers. The sum of the first two is 35 than the third.Find the integers
Answer by checkley77(7172)   (Show Source):
You can put this solution on YOUR website!
The sum of the first two is 35 [more or less]? than the third.
Add & resubmit.

Question 241937: The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible
even five-digit number. The digit in the tens place is
a. 1 b. 2 c. 3 d. 4 e. 9

Answer by Edwin McCravy(2938)   (Show Source):
You can put this solution on YOUR website!
9, choice e.
'
We use the smallest possible digit for the 10000s place, 1.
We use the next smallest possible digit for the 1000s place, 2.
We use the next smallest possible digit for the 100s place, 3.
We would use the next smallest number, 4 for the 10's place, but
since there are only two left, and the number has to be even, we
must save the 4 for the ones digit. So that leaves only 9 for
the tens digit. The 4 has to be the ones digit.
'
So the smallest such even number is 12394, and the digit in the
tens place is 9, choice e.
`
Edwin

Question 241664: one more than the difference between 18 and seven times a number is -9
Answer by College Student(266)   (Show Source):
You can put this solution on YOUR website!
This would be our equation:
Now let's solve for x:

.
Check:

.
Done!

Question 241703: Take the number 4, use it exactly 5 times, and come up with an equation for which the answer is 55.
Found 2 solutions by ly12603, Alan3354:
Answer by ly12603(37)   (Show Source):
You can put this solution on YOUR website!
the closest i cam come is 56. take 4 times 4 and that gives you 16. multiply that by 4 and get 64. subtract 4 from that and you get 60, 4 less tahn that is 56. if this is not the answer please tell me, im interested to know.

Answer by Alan3354(6153)   (Show Source):
You can put this solution on YOUR website!
Take the number 4, use it exactly 5 times, and come up with an equation for which the answer is 55.
--------
44 + 44/4 = 55
What's the point of this?

Question 241491: FIND Two consecutive integers such that half the smaller plus three times the larger is -32
Answer by checkley77(7172)   (Show Source):
You can put this solution on YOUR website!
Let x & x+1 be the 2 integers.
x/2+3(x+1)=-32
x/2+3x+3=-32
x/2+3x=-32-3
x/2+3x=-35
3.5x=-35
x=-35/3.5
x=-10 ans for the smaller integer.
-10+1=9 ans. for the larger integer.
Proof:
-10/2+3*9=-32
-5-27=-32
-32=-32

Question 241464: how many integers greater than 10 and less than one hundred are increased by nine when their digits are reversed
Answer by edjones(3330)   (Show Source):
You can put this solution on YOUR website!
8
12, 23, 34, 45, 56, 67, 78, 89.
.
Ed

Question 240987: one fourth of a number, decreased by 10, is -50. find the number
Answer by College Student(266)   (Show Source):
You can put this solution on YOUR website!
one fourth of a number, decreased by 10, is -50
.

.
Done! :)

Question 240334: what are two consecutive odd intergers such that twice the larger, increased by the smaller, is 43
Answer by College Student(266)   (Show Source):
You can put this solution on YOUR website!
what are two consecutive odd intergers such that twice the larger, increased by the smaller, is 43
.
Let x = integer
and x+2 = consecutive odd integer
.
The equation then becomes:

Now let's solve for x to find the smaller integer.

Now divide by 3 on both sides.
Then add two to find the consecutive odd integer.
Once that is done, plug in these values in the original equation to check/confirm the integers make sense for the equation.
.
Done! :)

Question 240345: if twelve is added to five times the number, the result exceeds twice the number by twenty seven. What is the number

Answer by College Student(266)   (Show Source):
You can put this solution on YOUR website!
If twelve is added to five times the number, the result =
exceeds twice the number by twenty seven
.
Our equation becomes:
.
Now you need to combine like terms and solve for x.
I suggest you group the x terms on the left and the integers on the right.
.
I'll let you do the algebra. You should come up with x=5.
.
Done! :)

Question 240952: the larger of two numbers is one less than three times the smaller. If three times the larger is five more than eight times the smaller, find the numbers.
Answer by dspence(2)   (Show Source):
You can put this solution on YOUR website!
8,23

Question 240547: I AM A WHOLE NUMBER HALF OF ME IS GREATER THAN 20, ONE OF MY DIGITS IS DOUBLE THE OTHER WHAT NUMBER AM I ? ONE OF DIGITS IS A PERFECT SQUARE.
Answer by ankor@dixie-net.com(6707)   (Show Source):
You can put this solution on YOUR website!
I AM A WHOLE NUMBER, HALF OF ME IS GREATER THAN 20, ONE OF MY DIGITS IS DOUBLE THE OTHER WHAT NUMBER AM I ?
ONE OF DIGITS IS A PERFECT SQUARE.
:
let x = the 10's digit
let y = the units digit
:
:
"One of the digits is double the other"
x = 2y
therefore we know x is an even number
:
"One of the digits is a perfect square"
1, 4,
:
number is either 48 or 84 (half is greater than 20)

Question 240772: There were 82 people at a family reunion.
There were 4 more men than women.
There were 10 more children than adults.
How many childern were there?
Answer by edjones(3330)   (Show Source):
You can put this solution on YOUR website!
w=number of women, w+4=numb of men, w+w+4+10=numb of kids
w+w+4+w+w+4+10=82
4w+18=82
4w=64
w=16
w+w+4+10=46
.
Ed

Question 240770: the numbers on karl's three raffle tickets are consecutive integers.The sum of the numbers is 138.What are the numbers? For me consecutive integers are hard to understand,but i did try to figure it out.This is how i did it:x+(x+1)=138, 2x+1=138,2x=137.of course if you divide 2 and 137 you will get a number that has a decimal in it,so then i wasn't sure what to do.
Answer by solver91311(5106)   (Show Source):
You can put this solution on YOUR website!

You only missed it by THAT much (holds thumb and forefinger a tiny distance apart)

Your method would have worked just fine if he had only two tickets (of course, in that case, the sum would necessarily have been odd). But he had three tickets, so you need three consecutive integers.

If you let represent the first integer, then is most certainly the next consecutive integer -- just as you stated. But you needed the next one as well, which is

Now, the sum of all three is 138, so:

Solve that and you will find that is a nice, tidy integer.

Write back and let me know how you did.

John

Question 240674: what are six consecutive integers starting with -4?

Answer by rapaljer(3631)   (Show Source):
You can put this solution on YOUR website!
-4, -3, -2, -1, 0, 1

Question 240709: The sum of four consecutive odd numbers is 40.Find the four numbers
Answer by Alan3354(6153)   (Show Source):
You can put this solution on YOUR website!
The sum of four consecutive odd numbers is 40.Find the four numbers
-------------
The easy way:
average = 40/4 = 10
2 numbers are less, 2 are more.
7,9,11,13

Question 240588: whats three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the number. Please show the work.
Answer by checkley77(7172)   (Show Source):
You can put this solution on YOUR website!
X+Y=21 OR X=21-Y
3X=4Y
3(21-Y)=4Y
63-3Y=4Y
-3Y-4Y=-63
-7Y=-63
Y=-63/-7
Y=9 ANS.
X=21-9=12 ANS.
PROOF:
3*12=4*9
36=36

Question 240618: The sum of the page numbers on consecutive pages of a book is 267.what are the page numbers? I had tried this problem but i wasn't understanding it at all.so this is what i tried to do:x+(x+1)=267,2x+1=267,2x=266.My answers were 133, and 134.
Answer by checkley77(7172)   (Show Source):
You can put this solution on YOUR website!
I get the same page numbers as follows:
x+x+1=267
2x=267-1
2x=266
x=266/2
x=133 ans. for the left hand page.
133+1=134 ans. for the right hand page.

Question 240653: The sum of two numbers is 5/4. One number is 1/2 of the other. Find the
product of these two numbers.
A. 25/72; B. 25/63; C. 5/8; D. 5/6; E. none
Answer by Theo(691)   (Show Source):
You can put this solution on YOUR website!
x + y = 5/4

x = .5*y

this makes:

y = 2*x

substituting in original equation gets:

x + 2*x = 5/4

combine like terms to get:

3*x = 5/4

divide both sides by 3 to get:

x = 5/12

y = 2x so:

y = 5/6

substitute in original equation of x + y = 5/12 to get:

5/12 + 5/6 = 5/12 + 10/12 = 15/12 = 5/4

since x = 5/12 and y = 5/6, the product of the two numbers is:

5/12 * 5/6 = 25/72

that would be selection A.

Question 240655: The units’ digit of a two digit number is twice the tens’ digit. If the digits
of the number were reversed the resulting number would be six less than
twice the original number. Find the original number.
A. 12; B. 24; C. 36; D. 48; E. none
Answer by stanbon(26367)   (Show Source):
You can put this solution on YOUR website!
The units’ digit of a two digit number is twice the tens’ digit. If the digits
of the number were reversed the resulting number would be six less than
twice the original number. Find the original number.
----
Let the original number be 10t+u
The reversed-digit number is 10u+t
---------------------
Equations:
u = 2t
10u+t = 2(10t+u)-6
--------------
Substitute for "u" and solve for "t":
10(2t)+t = 2(10t+2t)-6
21t = 24t-6
3t = 6
t = 2 (the ten's digit)
--------------------------------
Since u = 2t, u = 4 (the unit's digit)
======================================
Original number = 24
==========================================
Cheers,
Stan H.
A. 12; B. 24; C. 36; D. 48; E. none

Question 240661: the difference between two numbers is 16. three times the larger number is seven times the smaller
Answer by checkley77(7172)   (Show Source):
You can put this solution on YOUR website!
X-Y=16
X=16+Y
3X=7Y REPLACE X BY (16+Y)
3(16+Y)=7Y
48+3Y=7Y
3Y-7Y=-48
-4Y=-48
Y=-48/-4
Y=12 ANS. FOR THE SMALLER NUMBER.
X-12=16
X=16+12
X=28 ANS. FOR THE LARGER NUMBER.
PROOF:
3*28=7*12
84=84

Question 240645: One number is 4 more than twice the second number. Their total is 25. Find the numbers. I just need help on writing the problem, then I will be able to solve it.
Answer by rapaljer(3631)   (Show Source):
You can put this solution on YOUR website!
Let x= the 2nd number. (I always like to let x = the quantity at the end of the sentence or phrase!)

Now, the first number is 4 more than twice the second number, where the second number is x.

Therefore, first number = 2x+4.

Now the equation is that the total (or sum!) of the numbers is 25.
x+2x+4=25

You said that you can solve it, so go for it!

I have a LOT of resources on my own website on the topic of WORD PROBLEMS. To find my website, do a "BING" or a "GOOGLE" search for my last name "Rapalje". Near the top of the search list, you should see "Rapalje Homepage." Click on this, and look near the top of my homepage for the link "Basic, Intermediate and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in "Chapter 1" for "Sections 1.09 and 1.10, Word Problems." This is my own explanation especially written for students who have trouble understanding math. I wrote this to students, NOT mathematicians, and I think you will find it easier to understand than your own traditional textbooks!! In addition to this page, the entire website is supported by my "MATH IN LIVING COLOR" pages, where the hardest problems are solved IN COLOR.

If you like my website, please recommend it to family and friends who have trouble understanding math!! It's ALL FREE!!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

Question 240602: The sum of three consecutive odd integers is 279.What are the integers? I tried this problem but i wasn't sure if it was correct? Also i really didn't understand to much of it.This is how i did my problem:x+(x+3)=279,2x+3=279,2x=276
Answer by stanbon(26367)   (Show Source):
You can put this solution on YOUR website!
The sum of three consecutive odd integers is 279.
What are the integers?
---------------
1st: 2x-1
2nd: 2x+1
3rd: 2x+3
----------------------
Equation:
6x+3 = 279
6x = 276
x = 49
-------------
1st: 2x-1 = 97
2nd: 99
3rd: 101
========================
Cheers,
Stan H.

Question 240462: One number is 5 less than another. Five times the smalller number is 1 less than 3 times the larger. Find the numbers.
Answer by College Student(266)   (Show Source):
You can put this solution on YOUR website!
x = a number
x-5 = the other number
.
So our equation becomes:

Now solve for x to find one of the numbers.

.
Now find the other number by plugging this value in .
.
Remember to check your answers by plugging both numbers in the original equation. Both sides must equal to each other, otherwise you've done something wrong.
.
Done! :)

Question 240510: 10 less than the product of a number and three
Answer by College Student(266)   (Show Source):
You can put this solution on YOUR website!
Ten less than the product of a number and three: 3x-10
Is this all you need?

Question 240472: what is 631 to the 399th power divided by ten
Answer by Alan3354(6153)   (Show Source):
You can put this solution on YOUR website!
= ~ 1.628224699065E1116 (using Windows calculator)
----------
=

Question 240441: The sum of two consecutive even integers is 86. Find the larger number.
Answer by Alan3354(6153)   (Show Source):
You can put this solution on YOUR website!
The easy way:
86/2 = 43
One number is just below = 42
One is just above = 44