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

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Question 994779: half of a certain number plus 3 gives the same value as twice the number plus 7
Answer by ankor@dixie-net.com(18980)   (Show Source):
You can put this solution on YOUR website!
half of a certain number plus 3 gives the same value as twice the number plus 7
.5n + 3 = 2n + 7
3 - 7 = 2n - .5n
-4 = 1.5n
n = -4/1.5
n = -2 is the number
:
:
Check this in the original statement using n = -2.667
.5(-2.667) + 3 = 2(-2.667) + 7
-1.333 + 3 = -5.333 + 7
-1.667 = -1.667

Question 994771: The tens digit is odd the hundreds digit is twice the tenths digit,the tens digit the tenths digit and the thousandths digit a
re in the descending order from left to right. The hundreds digit, the ones digit and the hundredths digit are in ascending order from left to right. The tens digit is divisible by the tenths digit and the thousandths digit. No digit is used more then once

Answer by ankor@dixie-net.com(18980)   (Show Source):
You can put this solution on YOUR website!
The digits: a b c d . e f g
:
The tens digit is odd
the hundreds digit is twice the tenths digit,
b = 2e
:
the tens digit the tenths digit and the thousandths digit are in the descending order from left to right.
c, e, g
:
The hundreds digit, the ones digit and the hundredths digit are in ascending order from left to right.
b, d, f
:
The tens digit is divisible by the tenths digit and the thousandths digit.
c/e and c/g
The only odd digit divisible by another digit is 9
c = 9, then e and f are 3 and 1 or 1 and 3
descending order 9, 3, 1
:
we now have: a b 9 d . 3 f 1
:
we know that b = 2(3) = 6
we now have: a 9 6 d . 3 f 1
:
b, d, f ascending order b = 6, therefore
6, 7, 8
:
No digit is used more then once
:
Now we have: a 6 9 7 . 3 8 1
a? I guess there isn't a thousand digit,
I'm going to say 697.381 is the number

Question 994760: How can you use the predict and test strategy to solve this problems ?
Answer by stanbon(69061)   (Show Source):

Question 994695:  a waitress sold 17 ribeye steak dinners and 20 grilled salmon dinners, totalling $590.81 on a particular day. Another day she sold 24 ribeye steak dinners and 10 grilled salmon dinners, totaling$580.66. How much did each type of dinner cost?
Answer by Alan3354(47455)   (Show Source):

Question 994723: I really need some help with this problem, if anyone's not busy I would appreciate any help at all.
a waitress sold 17 ribeye steak dinners and 20 grilled salmon dinners, totalling $590.81 on a particular day. Another day she sold 24 ribeye steak dinners and 10 grilled salmon dinners, totaling$580.66. How much did each type of dinner cost?

Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(11324)   (Show Source):
You can put this solution on YOUR website!
let ribeye steak dinners be and grilled salmon dinners
if a waitress sold ribeye steak dinners and grilled salmon dinners, totaling $on a particular day, then we have .........eq.1 if another day she sold ribeye steak dinners and grilled salmon dinners, totaling$, then we have
.........eq.2
solve the system:
.........eq.1
.........eq.2...=> both sides multiply by
-------------------------------------------
.........eq.1
.........eq.2=> subtract eq.1 from eq.2
-----------------------------------------------------

now find
.........eq.2

How much did each type of dinner cost?
ribeye steak dinners cost and
grilled salmon dinners cost

Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
a waitress sold 17 ribeye steak dinners and 20 grilled salmon dinners, totalling $590.81 on a particular day. Another day she sold 24 ribeye steak dinners and 10 grilled salmon dinners, totaling$580.66. How much did each type of dinner cost?
------------
17r + 20s = 59081
24r + 10s = 58066 x2 --> 48r + 20s = 116132
----
17r + 20s = 59081
48r + 20s = 116132
-------------------------- Subtract
-31r = -57051
r = 1840.355 --> $18.40 Can you solve for s? Question 994720: a waitress sold 17 ribeye steak dinners and 20 grilled salmon dinners, totalling$590.81 on a particular day. Another day she sold 24 ribeye steak dinners and 10 grilled salmon dinners, totaling $580.66. How much did each type of dinner cost? Answer by macston(4006) (Show Source): You can put this solution on YOUR website! . R=cost of rib-eye dinner; S=cost of salmon dinner . 24R+10S=$580.66
10S=$580.66-24R 20S=$1161.32-48R Use this to substitute for 20S below
.
17R+20S=$590.81 . Substitute for 20S. 17R+($1161.32-48R)=$590.81 -31R=-$570.51
R=$18.40 ANSWER 1: Rib-eye dinner costs$18.40.
.
24R+10S=$580.66 24($18.40)+10S=$580.66$441.60+10S=$580.66 441.69 10S=$139.06
S=$13.91 ANSWER 2: A salmon dinner costs$13.91.
.
CHECK:
.
17R+20S=$590.81 17($18.40)+20($13.91)=$590.81
$312.80+$278.20=$590.81$591=$590.81 19 cent discrepancy from rounding to nearest cent. Question 994696: A train travels 110 km in the same time that a plane covers 385km. If the speed of the plane is 20 km per hr less than 4 times the speed of the train, find both speeds. Answer by josmiceli(13716) (Show Source): You can put this solution on YOUR website! Let = the speed of the train in km/hr = the speed of the plane in km/hr -------------------- Equation for train: (1) Equation for plane: (2) ---------------------- (2) and (1) ----------------- By substitution: (2) (2) (2) (2) and ----------------- The speed of the train is 40 km/hr The speed of the train is 140 km/hr ----------------- check: (2) (2) (2) and (1) (1) (1) OK Question 994699: I need your help with this word problem :( A motor scooter travels 16 mi in the same time that a bicycle covers 7 mi. If the rate of the scooter is 5mph more than twice the rate of the bicycle, find both rates. Answer by Boreal(1464) (Show Source): You can put this solution on YOUR website! bicycle rate is x mph scooter rate is 2x+5 mph 2x+5 mph * y hours=16 mi. y=16/(2x+5) also x mph * y hours=7 miles y=7/x. So, (16/(2x+5))=(7/x) cross multiply 16x=7(2x+5) 16x=14x+35 2x=35 x=17.5 mph bicycle 2x+5=40 mph scooter ======== scooter travels 16 miles at 40 mph, that is 0.4 hours or 24 minutes. bicycle travels 7 miles at 17.5 mph, that is 7/17.5 hours, and that is 0.4 hours or 24 minutes. Question 994701: Write an equation in the slope - intercept form of the line that satisfies the given conditions. Through (9,3); parallel to 3x-y=5 The equation of the line is? Answer by Boreal(1464) (Show Source): You can put this solution on YOUR website! Parallel lines have the same slope. slope of the first line is 3x-y=5 y=3x-5; slope is 3. So, we have a line with slope 3 passing through the point (9,3) point slope formula is y-y1=m(x-x1) y-3=3(x-9) y-3=3x-27 y=3x-24 Question 994673: Two angles are complementary and the larger one is 14 degrees more than that 3 times the smaller one. Find the angles. Answer by Boreal(1464) (Show Source): You can put this solution on YOUR website! smaller angle =x larger=3x+14 sum is 90 degrees 4x+14=90 4x=76 x=19 degrees 90-x=71 degrees, and that is 3 times the smaller (57) +14. angles are 19 and 71 degrees Question 994639: will the number (-2)times(-2)consisting of 350(-2)'s be a positive or negative number? Answer by Alan3354(47455) (Show Source): Question 994605: similarity between 85, 17, 19, 4, 2 Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! They're all less than 1000. Question 994598: The sum of two number is 90. The larger is 14 more than 3 times the smaller number. Find the number. Answer by macston(4006) (Show Source): You can put this solution on YOUR website! . S=smaller number; L=larger number=3S+14 . S+L=90 S+(3S+14)=90 4S+14=90 4S=76 S=19 L=3S+14=3(19)=14=57+14=71 . ANSWER: The two numbers are 19 and 71. . CHECK: S+L=90 19+71=90 90=90 . Question 994573: The sum of two numbers is 30. Six less than twice the smaller number is equal to the number x. Find the larger number. Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! You get two different answers depending on whether x is the larger or the smaller number. Your problem is stated ambiguously. John My calculator said it, I believe it, that settles it Question 994522: The sum of 2 numbers is 94 and their difference is 122. Find these numbers Found 2 solutions by MathTherapy, macston: Answer by MathTherapy(4047) (Show Source): You can put this solution on YOUR website! The sum of 2 numbers is 94 and their difference is 122. Find these numbers Numbers:  Answer by macston(4006) (Show Source): You can put this solution on YOUR website! . x and y are two numbers . x-y=122 x=122+y . x+y=84 (122+y)+y=84 2y=-38 y=-19 x=122+y=122-19=103 ANSWER: The numbers are 103 and -19 . CHECK: x+y=84 103+(-19)=84 84=84 . Question 994553: what number is 17 less than a quarter million Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! What is it that you don't understand about this problem? Do you not know the meaning of "quarter million" or are you having trouble with the concept of "less than"? John My calculator said it, I believe it, that settles it Question 994402: the sum of four consecutive integers is -106. find the integers Answer by Cromlix(3061) (Show Source): You can put this solution on YOUR website! Hi there, 4 consecutive integers = n, n + 1, n + 2, n + 3. n +(n + 1) + (n + 2) + (n + 3) = - 106 Remove brackets: n + n + 1 + n + 2 + n + 3 = - 106 Collect like terms 4n = -106 - 6 4n = -112 n = -112/4 n = -28. 4 consecutive integers :- -28, -27, -26, -25. Hope this helps :-) Question 994286: what 2 numbers equal 10 when added together but, equal 100 when multiplied? Answer by josgarithmetic(13975) (Show Source): You can put this solution on YOUR website! - Formula for general solution of a quadratic equation, --------Complex but not Real Number. No solution for this case. Question 994139: Twice a number added to thrice the same number equals 100. What is d number? Answer by josmiceli(13716) (Show Source): You can put this solution on YOUR website! The number is 20 Question 994145: Find the number such that when 3/4 of it is added to 3whole no 1/2 the sum is the such a when 2/3 of it is subtracted from 6whole no 1/2 Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! Find the number such that when 3/4 of it is added to 3whole no 1/2 the sum is the such a when 2/3 of it is subtracted from 6whole no 1/2 ----- Equation: (3/4)x + 3 1/2 = 6 1/2 - (2/3)x ----- (3/4)x + (7/2) = (13/2) - (2/3)x ---- [(3/4)+(2/3)]x = (13/2)-(7/2) ------ [(9-8)/12]x = 3 ---- x = 36 ------ Cheers, Stan H. ----------- Question 994130: the denominator of a fraction exceeds its numerator by 3. if the numerator is decreased by 1 and the denominator is increased by 3, the value of the resulting fraction is 1/2. Answer by Theo(5548) (Show Source): You can put this solution on YOUR website! (x-1) / (x+6) = 1/2 multiply both sides of this equation by (x+6) to get: (x-1) = 1/2 * (x + 6) multiply both sides of this equation by 2 to get: 2x-1 = x+6 add 1 to both sides of this equation and subtract x from both sides of this equation to get: 2x - x = 6 + 1 combine like terms to get: x = 7 when x = 7, (x-1) / (x+6) becomes 7/14 which is equal to 1/2. the original fraction of x / (x+3) must be equal to 8 / 11. subtract 1 from the numerator of 8 and you get 7. add 3 to the denominator of 11 and you get 14. if i understood what you are looking for, the solution appears to be x = 8. Question 994026: A number multiplied by -2, subtracted from the sum of 14 and five times the number Answer by ikleyn(988) (Show Source): You can put this solution on YOUR website! . A number multiplied by -2, subtracted from the sum of 14 and five times the number. -------------------------------------------------------------------- (14 + 5x) -2x Question 994079: what two numbers add to get 5 and multiply to get -6? Answer by jim_thompson5910(33401) (Show Source): You can put this solution on YOUR website! 6 and -1 fit the description 6 + (-1) = 5 6 times -1 = -6 Question 993861: Mr. Parker invested a part of$54,000 at nine and one-half percent and the rest is at 12%. His annual income from the 12% investment is three times as large as that from the nine and one-half percent investment. How much does he invest at each rate?
Answer by lwsshak3(11500)   (Show Source):
You can put this solution on YOUR website!
Mr. Parker invested a part of $54,000 at nine and one-half percent and the rest is at 12%. His annual income from the 12% investment is three times as large as that from the nine and one-half percent investment. How much does he invest at each rate? let x=amt invested at 9.5 % rate 54000-x=amt invested at 12 % rate 12%*(54000-x)=3*9.5%x 6480-.12x=.285x. .405x=6480 x=$16000
54000-x=$38000 amt invested at 9.5 % rate=$16000
amt invested at 12 % rate=$38000 Question 993923: 1. 5 less than 10 2. 5 more than 10 Answer by Alan3354(47455) (Show Source): Question 994015: the sum of three number is 55. the difference of the largest and the smallest is 51, and the sum of the two smaller number is 12. find the numbers. Answer by ikleyn(988) (Show Source): You can put this solution on YOUR website! . x + y + z = 55, (1) x - z = 51, (2) y + z = 12. (3) where x is the largest number and z is the smallest one. Now, distract (3) from (1). You will get x = 55 - 12 = 43. Substitute it into (2), and you will find z = 43 - 51 = -8. Substitute z = -8 into (3), and you will find y = 12 + 8 = 20. Answer. x = 43, y = 20, z= -8.  Question 994029: The Difference of six times a number and 7 is -49 Answer by rfer(15570) (Show Source): You can put this solution on YOUR website! 6x-7=-49 6x=-49+7 x=-42/6 x=-7 Question 994000: what is eleven more than six Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! what is eleven more than six ------ Ans:: 6 + 11 = 17 ------ Cheers, Stan H. ------ Question 993932: Find two numbers with a sum of 14 and a product of 40 Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! Find two numbers with a sum of 14 and a product of 40 --------------- Try pairs of factors of 40. ---- 1*40 NG 2*20 NG etc Question 993262: 2 numbers that sum of them is 26 and when you multiply them is 315 Answer by farohw(153) (Show Source): You can put this solution on YOUR website! Let x + y = 26 represent the sum of two numbers is 26, and x*y = 315 for the product of 315. x + y = 26 --> y = 26 - x By substitution, x*y = 315 --> x*(26 - x) = 315 26x - x^2 = 315 --> x^2 - 26x - 315 = 0 becomes (x - 35)(x + 9) = 0 when you factor. Thus, x - 35 = 0 and x + 9 = 0 yields x = 35, x = -9 So if you add 35 + (-9) = 26 However, when you multiply 35*(-9) = -315 not 315. Question 993781: Please help me solve the following equation: A rectangle has a width of 6 inches and a perimeter of 26 inches. What is the LENGTH of the rectangle? Answer by rfer(15570) (Show Source): You can put this solution on YOUR website! 26-(2*6)=14 14/2=7 inches Question 993758: The sum of 2 numbers is 110. The larger number is 2 less than 7 times the smaller. Find the larger number Answer by MathLover1(11324) (Show Source): You can put this solution on YOUR website! let numbers be and , and let be larger number if the sum of numbers is , we have .........eq.1 if the larger number is less than times the smaller number we have ......eq.2 to find the larger number equal the right sides of eq.1 and eq.2: .........solve for => larger number and smaller number is: Question 993589: What is the similarity between the numbers 85,17,19,4 and 2 Answer by Alan3354(47455) (Show Source): Question 993512: The sum of four consecutive numbers is -190. Please help me find the integers, thank you! Answer by Boreal(1464) (Show Source): You can put this solution on YOUR website! The numbers are x, x+1,x+2, and x+3 They add to -190 Their sum is 4x +6 4x+6= -190 4x= -196 x= -49, dividing by 4 the numbers are -49, -48,-47, and -46 They add to - 190 Question 993429: Hello can you help me with my algebra 1 homework, i have 3 problems i'm stumped on. 1) you charge$2 plus $0.50 per child for every hour you babysit. You earn$3.50 an hour when you watch the Crandell children. How many children are in the family?
2) There are 2 numbers whose sum is 72. 2 number is twice the other. what are the numbers?
3) Ryan ans Steve worked as electricians at $14 and$12 per hour respectively. One month Ryan worked 10 hours more than Steve. If their total income for the month was $3520, how many hours did each work during the month? Thanks alot for your help. Found 2 solutions by Cromlix, addingup: Answer by Cromlix(3061) (Show Source): You can put this solution on YOUR website! Hi there, 1) 2 +$0.50x = $3.50$0.50x = $3.50 -$2
$0.50x =$1.50
x = $1.50/$0.50
x = 3
3 Children.
2) 2 numbers
use x + 2x
x + 2x = 72
3x = 72
x = 72/3
x = 24
Numbers are 24 and 48
3) Steve's amount of work - 12x
Ryan's amount of work = 14x + 10
12x + 14x + 10 = $3520 28x + 10 =$3520
28x = $3520 - 10 28x =$3510
x = $135 Steve earned 12(135) =$1620
Ryan earned 14(135) + 10 = $1900 Hope this helps :-) Answer by addingup(248) (Show Source): You can put this solution on YOUR website! 1)Your rate per hour is a flat fee of$2 plus 0.50 per child. Let's call the number of children n:
2+0.50n= 3.50 subtract 2 from both sides
0.50n= 1.50 divide both sides by 0.50
n= 3 The Crandells have 3 kids.
---------------
2) There are 2 numbers whose sum is 72. One number is twice the other. Let's call the smaller number x, and the problem says the other number is 2x (twice the other):
x+2x= 72 Add the x:
3x= 72 Divide both sides by 3
x= 24 is the smaller number, and the other is 2×24= 48
--------------------
3) Ryan & Steve make $14 and$12. One month Ryan worked 10 hours more than Steve. If their total income for the month was \$3520, how many hours did each work.
Let's call Steve's hours x and Ryan's, the problem says, is x+10
12x+14(x+10)= 3,520 Multiply on left:
12x+14x+140= 3,520 Add x on left and subtract 140 on both sides
26x= 3,380 Now divide both sides by 26
x= 130 are the hours Steve worked. and Ryan worked 10 hours more: 130+10=140
Proof
130×12= 1560
140×14= 1960
.......------
=======3,520 We have the correct answer

Question 993400: 1) Twice a number increased by 12 is equal 31 less then three times the number. Find the number
2) 8-2 times a number is equal to the number plus 17. Find the number.
3) The perimeter of a rectangle is 24in. Find the dimensions if its length is 3in greater than its width.
4) 1/5th of a number plus 5 times that number is equal to seven times the number less 18. Find the number
5) The perimeter of a rectangle is 12. The lenght is 2 more than twice its width. Find the dimensions of the rectangle

Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
1).
2x+12=3x-31
43=x
.
2).
8-2x=x+17
-9=3x
-3=x
.
3).
W=width; L=length=W+3
.
P=2(L+W)
24=2((W+3)+W)
12=2W+3
9=2
4.5=W ANSWER 1: The width is 4.5 inches
L=W+3=4.5+3=7.5 ANSWER 2: The length is 7.5 inches.
.
CHECK:
P=2(L+W)
24in=2(7.5in+4.5in)
24in=2(12in)
24in=24in
.
4).
x/5+5x=7x-18
x/5+25x/5=7x-18
26x/5=7x-18
5.2x=7x-18
18=1.8x
10=x
ANSWER: The number is 10.
.
CHECK:
x/5+5x=7x-18
(10/5)+5(10)=7(10)-18
2+50=70-18
52=52
.
IN THE FUTURE, PLEASE LIMIT TO ONE QUESTION PER POST.
Otherwise, it seems like you are just dumping your
homework here without trying.

Question 993261: The sum of three numbers is 26 if the second number is 3 more than four times the first number and the third number is 5 less than twice the first number find the number
Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
F=first number; S=second number; T=third number
.
S=4F+3
.
T=2F-5
.
F+S+T=26
F+(4F+3)+(2F-5)=26
7F-2=26
7F=28
F=4
S=4F+3=4(4)+3=16+3=19
T=2F-5=2(4)-5=8-5=3
.
ANSWER: The numbers are 4,19, and 3
.
CHECK:
F+S+T=26
4+19+3=26
26=26

Question 993374: One number is 3 greater than another. The product of the numbers is 130. What are the numbers?
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
One number is 3 greater than another. The product of the numbers is 130. What are the numbers?
---------------
Find a pair of factors of 130 that differ by 3.

Question 993347: What is the similarity between 85 17 19 4 and 2
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
They're all positive.

Question 993357: Please help me with this please :A number is two times the sum of two other
Numbers, a and b, number a is three less than four times
b. Write an expression for the sum of the three
Numbers. Simplify using algebra tiles.(( I have this
But I'm not100% sure, 2x=4x-3))

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
A number is two times the sum of two other
Numbers, a and b, number a is three less than four times
b. Write an expression for the sum of the three
Numbers. Simplify using algebra tiles.
-------
x = 2(a+b)
a = 4b-3
----
Substitute for "a" to get:
x = 2(4b-3 + b) = 10b-6
-------
Sum = x + a + b
Sum = 10b-6 + 4b-3 + b
Sum = 15b - 9
-----------------
Cheers,
Stan H.
===========

Question 993353: What number is 3,500 more than the product of 780 and 56? The answer is 17,180. I need formula.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(47455)   (Show Source):
You can put this solution on YOUR website!
What number is 3,500 more than the product of 780 and 56? The answer is 17,180. I need formula.
================
n = 780*56 + 3500
n = 47180

Answer by stanbon(69061)   (Show Source):
You can put this solution on YOUR website!
What number is 3,500 more than the product of 780 and 56?
The answer is 17,180. I need formula.
-----
Let the number be "x"::
780*56 = x + 3500
-----
Cheers,
Stan H.