# Questions on Word Problems: Miscellaneous Word Problems answered by real tutors!

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Question 994728: I buy 30 ft3 of stuffing for a crafts project, but the instructions are in in3. How many in3 of fabric do I have?
You can put this solution on YOUR website!

Since one linear foot equals , the cube measures wide by deep by high. To compute the volume in cubic inches, multiply the length, width, and height.
So, .

The area of a rectangular lot is to be 1456 quare feet. If the width of the lot is 24 feet less than the length, what is the dimention of the lot?

You can put this solution on YOUR website!
The area of a rectangular lot is to be 1456 square feet. If the width of the lot is 24 feet less than the length, what is the dimention of the lot?
---------------------
length:: x ft
width:: x-24 ft
-----
Equation:
x(x-24) = 1456
---------
x^2 - 24x - 1456 = 0
-----
x = 52 ft (length)
x-24 = 28 ft (width)
---------------------
Cheers,
Stan H.
----------

Question 994635: Don and Jacob want to know who reads more pages per hour. Don keeps track of the number of pages he reads in a graph, and Jacob keeps track of how many pages he reads in a table.

How many pages per hour does each boy read, and who reads at a faster rate?

Don:
pages per hour

Jacob:
pages per hour

The person who reads faster is:
(Type D for Don or J for Jacob)

You can put this solution on YOUR website!
to find pages per hour, divide the pages by the hours.

Question 994582: Water is poured into a conical paper cup at the rate of 3/2 in^3/sec . If the cup is 6 inches tall and the top
has a radius of 3 inches, how fast is the water level rising when the
water is 3 inches deep?
The water level is rising at a rate of____
Thank you

You can put this solution on YOUR website!
The volume of a cone of height and radius is given by
.
I am not going to keep mentioning units,
but time, is understood to be measured in seconds;
and are understood to be measured in inches,
and is understood to be in cubic inches.
The cup is filling at a rate of .
As the water is filling the conical paper cup,
the water is in the shape of a similar cone,
with a radius to height ratio of ,
so .
The volume of water in the cup as a function of the water-cone height is
.
The inverse function is

When , ;
, and

Question 994569: Sandy bought a soft drink for $2 and four candy bars.She spent a total of$14.How much did each candy bar cost?

Found 2 solutions by stanbon, solver91311:
You can put this solution on YOUR website!
Sandy bought a soft drink for $2 and four candy bars.She spent a total of$14.How much did each candy bar cost?
-------
Equation:
14 = 2 + 4*c
----
4c = 12
----
c = $3 (price of each Candy bar) ------ Cheers, Stan H. ========== Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! Hint: How much did she have left from the$14 after she bought the $2 soda? John My calculator said it, I believe it, that settles it Question 994513: Very confused on how to solve this related rates problem: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4 √(t) cm^3. After 64 seconds the radius of the balloon is r = How fast is the radius changing after 64 seconds? dr/dt = Thank you! Answer by rothauserc(2272) (Show Source): You can put this solution on YOUR website! Volume(V) = 4 * square root(t) and the volume of a sphere is (4/3)*pi*r^3 ******************************************************** after 64 seconds V = 4 * square root(64) = 32 now we use the second equation 32 = (4/3)*pi*r^3 multiply both sides of = by 3 96 = 4*pi*r^3 divide both sides of = by 4 pi*r^3 = 24 divide both sides of = by pi r^3 = 24 / pi = 7.639437267 ********************************************************* r = (7.639437267)^(1/3) = 1.969490044 cm ********************************************************* (4/3)*pi*r^3 = 4 * square root(t) divide both sides of = by 4 (1/3)*pi*r^3 = square root(t) multiply both sides of = by 3 pi*r^3 = 3*square root(t) divide both sides of = by pi r^3 = (3*t^(1/2)) / pi r = 0.954929659 * t^(1/6) approx t^(1/6) dr/dt = 1 / t^(5/6) Question 994516: a bag of fertilizer covers 3000 square feet of lawn .how many bags should be purchased to cover a rectangular lawn 240 feet by 120 feet Answer by macston(4006) (Show Source): You can put this solution on YOUR website! . ((240ft)(120ft))/(3000ft^2/bag)=9.6 bags ANSWER: The lawn requires 9.6 bags. . Question 994483: There are 18 more sophomores than juniors in an algebra class. If there are 78 students in this class, find the number of sophomores and the number of juniors in the class. Answer by macston(4006) (Show Source): You can put this solution on YOUR website! . If all students are sophomores or juniors: . J=number of juniors; S=number of sophomores=J+18 . J+S=78 J+J+18=78 2J=60 J=30 ANSWER 1: There are 30 juniors in the class. S=J+18=30+18=48 ANSWER 2: There are 48 sophomores in the class. . CHECK: J+S=78 30+48=78 78=78 Question 994321: Tom can watch 44 plates in three minutes. How many seconds will take them to wash 12 plates Answer by josmiceli(13716) (Show Source): You can put this solution on YOUR website! min sec HJe can wash 12 plates in 49.1 sec Question 994322: If 2 students in the typing pool can type 210 pages in 3 days,how many students needed to type 700 pages in 2 days Answer by MathTherapy(4047) (Show Source): You can put this solution on YOUR website! If 2 students in the typing pool can type 210 pages in 3 days,how many students needed to type 700 pages in 2 days  students  Question 994013: related rates problem: The spool of a kite is held fixed at 5 feet above the ground. The kite is 105 feet above the ground and traveling eastward in a horizontal fashion. The string is being let out at 2ft/sec. Find the horizontal speed of the kite when 125 feet of string are let out. Please explain how to set one of these type problems up. Very confused here. Thank you Found 2 solutions by KMST, stanbon: Answer by KMST(3791) (Show Source): You can put this solution on YOUR website! I almost agree with stanbon, but is the ratio of increase in horizontal distance to increase in string length. In other words, the kite travels horizontally per of string released. Since string is being released at , the horizontal speed of the kite (in ft/s) when 125 feet of string are let out is Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! The spool of a kite is held fixed at 5 feet above the ground. The kite is 105 feet above the ground and traveling eastward in a horizontal fashion. The string is being let out at 2ft/sec. Find the horizontal speed of the kite when 125 feet of string are let out. --------------- Draw the picture:: You have a right triangle with spool at (0,5), base = h, height = 100, hypotenuse = string = s ----- h^2 = s^2-100^2 ---- h = sqrt[s^2-100^2) ----- dh/ds = (1/2)(s^2-100^2)^(-1/2)*(2s) ----- dh/ds = s/sqrt[s^2-100^2) ----- h'(125) = 125/sqrt[125^2-100^2] = 125/75 = 5/3 = 1.67 ft/sec ---------- Cheers, Stan H. Question 994252: Mountain climber Joe climbed to a mountain peak that was1200 feet above its base and 1500 feet east of its base. Mountain climber Bob climbed to a mountain peak that was 900 feet above its base and 1000 feet east of its base. Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! And then what? Question 994144: daniel is 30 years old and meg is 22 years old. how many years ago was daniel twice as old sa meg? Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! daniel is 30 years old and meg is 22 years old. how many years ago was daniel twice as old sa meg? ----- Equation: (30+x) = 2(22+x) ---- 30+x = 44+2x x = -14 ----- Ans: 14 years ago, daniel was twice as old as meg Daniel was 30-14 = 16 and meg was 22-14 = 8 ---------- Cheers, Stan H. -------------- Question 994094: 19 824 tickets were sold for a rock concert. If they needed to sell 1 million dollars worth of tickets, about how much would each ticket need to be? Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! Divide the amount of money needed by the number of tickets sold. John My calculator said it, I believe it, that settles it Question 994068: Denzel's first three test scores in math or 90 190 what must Denzel score on his fourth test to keep his mean score at 90 or higher Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! Denzel's first three test scores in math or 90 190 what must Denzel score on his fourth test to keep his mean score at 90 or higher ---- You did not list the 3 test scores. Cheers, Stan H. --------- Question 994069: After the first three, the next would be 61. You'll want to do that again then add one hundred 63 Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! I don't get it. Question 994039: in a cage there are pigeons and rabbits of there are 20 heads and 48 feet, then how many rabbits are there ? Answer by Boreal(1464) (Show Source): You can put this solution on YOUR website! x=pigeons y=rabbits x+y=20 2x+4y=48 ======= 2x+4y=48 -2x-2y=-40 (multiply it by -2) 2y=8 y=4 rabbits x=16 pigeons that is 20 heads and 4*4+16*2=48 as a check Question 994014: A particle is moving around the ellipse 4x^2+16y^2 = 64. At any time t its x and y coordinates are given by x = 4cos(t) and y = 2sin(t). At what rate is the particle's distance to the origin changing when t = π/4? I know this is a related rates problem. But I don't know how to set this problem up in order to solve. Thank you Answer by KMST(3791) (Show Source): You can put this solution on YOUR website! I would think this is a calculus problem. The distance to the origin as a function of (time) is The function showing the rate of change at time is , and it can be calculated using the chain rule with and , and Applying the chain rule again, and again, to both terms: and . So, , and . Substituting the expression for , For , -->-->--> -->-->-->--> Question 993938: Cody built a pyramid of Lego. He rectangular Lego that were four bumps by two bumps. He started with one Lego in the top level. Underneath that he put in as many Lego as needed to leave one row of bumps all the way around the outside on each level. He was able to make ten layers on his pyramid before he ran out of Lego. The inside of the pyramid is completely filled in with Lego, many which are not visible to someone looking at the top of the pyramid. a. How many Lego are in the Pyramid? b. How many bumps total on all levels are visible on the outside of the pyramid? c. If Cody had an infinite supply of Lego, how many total bumps on all levels would be visible in a pyramid with "n" layers of Lego? Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! Re: part c. The number of exposed bumps on the nth level is 8n. Hence the total number of exposed bumps on an -level pyramid is: John My calculator said it, I believe it, that settles it Question 993862: A florist sells roses for$1.50 each and carnations for $0.85 each. Suppose you purchase a bouquet of 1 dozen flowers consisting of roses and carnations. A) Let x represent the number of roses purchased. Write an expression in terms of x that represents the number of carnations purchased. B) Write the expression that represents the cost of purchasing the carnations. Answer by fractalier(2141) (Show Source): You can put this solution on YOUR website! Well if there were a dozen purchased, and x of them are roses, then 12-x is the number of carnations. Their cost would be the cost of each carnation times the number purchased: ($0.85)(12 - x)

Question 993920: aiden typed h words in 3 hours how many words per minute did aiden type?

You can put this solution on YOUR website!
aiden typed h words in 3 hours.

3 hours is equal to 180 minutes.

therefore aiden typed h words in 180 minutes.

this means that aiden typed h/180 words in 1 minute.

to see if this makes sense, assume h is equal to 14,400.

aiden typed 14,400 words in 3 hours.

3 hours is equal to 180 minutes.

this means that aiden typed 14,400 words in 180 minutes.

divide 14,400 by 180 minutes and you get that aiden typed 14,400 / 180 words in 1 minute.

14,400 / 180 is equal to 80, so aiden typed 80 words in one minute.

it makes sense to me.

hopefully it will make sense to you as well.

Question 993944: A ball rolls off a desk at a speed of 3.0 m/s and lands .40 seconds later.
a) how far from the base of the desk does the ball land?

You can put this solution on YOUR website!
A ball rolls off a desk at a speed of 3.0 m/s and lands .40 seconds later.
a) how far from the base of the desk does the ball land?
---------------
3 m/sec * 0.4 sec = 1.2 meters

Question 993858: Hi
how many complete circles of 4cm radius can be cut from a fabric measuring 5m by 1.3m.
thank you

Found 2 solutions by ikleyn, jhunjiro:
You can put this solution on YOUR website!
.
The previous solution
http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.993858.html
is totally wrong!

To estimate the numbers of circles,  you should divide the area of the fabric  5 m x 1.3 m
(or,  better,  4.96 m x 1.28 m)  by the area of the  square  with the side of  8 cm.

You have   = 62  sizes of the square along the the longer side of the fabric and   = 16
sizes of the square along the shorter sides.  In total,  there are  62*16 = 992  such squares.

There is another pattern,  which seems more promising.  It is the pattern where the centers
of circles are located in the vertices of equilateral triangles.  Although it is elementary to analyse
such a pattern,  it seems to be still above of the average school level,  therefore
I am not placing such an analysis here.

You can put this solution on YOUR website!
Calculate for the area of the circle and fabric
area of the circle = pi*r^2
= pi*4^2
= 50.27 cm^2
area of the fabric = L*W
= 5*1.3 m
= 6.5 m^2
since the area of the circle is in cm convert the area of the fabric to cm
6.5 m^2 *( (100)^2 cm^2 / m^2 )
area of fabric in cm = 65000 cm^2

To get how many circles of 4cm radius can be cut JUST divide the area of fabric to the area of the circle
= 65000/50.27
total circle = 1293 :D
P.S just get the whole number :D

Question 993753: A ship left a port and sailed east at a rate of 20 mph. one hour later a second ship left the same port at the rate of 25 mph, also headed east. In how many hours did the second ship over take the first ship?
You can put this solution on YOUR website!
A ship left a port and sailed east at a rate of 20 mph. one hour later a second ship left the same port at the rate of 25 mph, also headed east. In how many hours did the second ship over take the first ship?
let x=travel time of 2nd ship
x+1=travel time of 1st ship
20(x+1)=25x
20x+20=25x
5x=20
x=4
In how many hours did the second ship over take the first ship? 4

Question 993755: A hog weighs twice as much as a sheep. Together they total 285 kg. How much does each weigh?

Question 993669: There are two types of tickets for a school play, the total cost for one student ticket and one general ticket is $11, the total cost for 14 student tickets and 9 general tickets is$119 how much does a student ticket cost?
You can put this solution on YOUR website!
There are two types of tickets for a school play,
let g = the general admission cost
let s = the student ticket cost
:
the total cost for one student ticket and one general ticket is $11, g + s = 11 : the total cost for 14 student tickets and 9 general tickets is$119
9g + 14s = 119
Multiply the 1st equation by 9 and subtract from the above equation
9g + 14s = 119
9g + 9s = 99
-----------------Subtraction eliminates g, find s
5s = 20
s = 20/5
s = $4 is the cost of the student ticket. : : Check this out, general admission: g = 11-4 =$7
9(7) + 4(14) =
63 + 56 = 119

Question 993690: there are two types of tickets for a school play thethe total cost for one student ticket and one general ticket is $11. the total cost for 14 student tickets 9 general tickets is$119. how much does a student ticket cost?
You can put this solution on YOUR website!
x=student ticket
y=general ticket
x+y=11
14x+9y=119
-9x-9y=-99, multiplying the first by -9. Now add the two:
5x=20
x=$4 per student ticket y=$7 per general ticket
14x=70
9 y=49
sum=$119 Question 993673: Fine the measure of an angle such that the sum of the measures of its compliment and its supplement is 118 degrees. Answer by fractalier(2141) (Show Source): You can put this solution on YOUR website! Okay...the complement of an angle is 90-x. The supplement is 180-x. Thus, (90-x)+(180-x)=118 270-2x=118 Subtracting 270 and dividing by -2 gives -2x = -152 x = 76 Question 993672: From a point on a straight road, two cars are driven opposite directions, one at 50miles per hour and the other 40 miles per hour. in how many hours will they be 450 miles apart? Answer by Cromlix(3061) (Show Source): You can put this solution on YOUR website! Hi there, Distance = 450 miles Speeds = 50 and 40 mph 50 + 40 = 90 450/90 = 5 In 5 hours they will be 450 miles apart (5 x 50) + (5 x 40) 250 + 200 = 450 Hope this helps :-) Question 993628: A cell company charges a monthly fee of 100 pesos for the first 1000 text messages, and 1 peso for each additional text message. Karen's bill for text messages for the month of May is 385 pesos. How many text messages did she send that month? Answer by Cromlix(3061) (Show Source): You can put this solution on YOUR website! Hi there, First take the 100 pesos which equals 1000 texts This leaves a charge of 285 pesos, which at 1 peso per text = 285 texts. In total Karen sent 1,285 texts. Hope this helps :-) Question 993466: A rectangular flower garden has a length that is 3 feet less than twice it's width. A 3 foot brick border is added around the garden, and the area of the garden and the brick border is a total of 221 square feet. Find the dimensions of the garden without the brick border. Answer by josgarithmetic(13975) (Show Source): You can put this solution on YOUR website! w and L, garden dimensions. u, the uniform width of the border around the garden. according to the description. , the border path's area. Total Area, Border Area, Simplify this A equation, at least partially: Substitute for L according to the description. .......Can you take this the rest of the way? Question 993463: A salesperson's weekly paycheck is 50% less than a second salesperson's paycheck. The two paychecks total$1125. Find the amount of each paycheck. (Round your answers to the nearest cent.)
You can put this solution on YOUR website!
.
S=second salesperson's check; F=first salesperson's check=0.5S
.
F+S=$1125 0.5S+S=$1125
1.5S=$1125 S=$750
F=0.5S=(0.5)($750)=$375
ANSWER: The first person's check was $375, and the second person's check is$750.
.
CHECK:
F+S=$1125$375+$750=$1125
$1125=$1125

Question 993401: A stone is thrown vertically upward from the roof of a building. The formula that describes the height h (in feet) of the stone after "t" seconds is given below.
h=-16t^2+64t+40
How many seconds after the stone is thrown would it reach for the first time 100 feet in height?

You can put this solution on YOUR website!
A stone is thrown vertically upward from the roof of a building. The formula that describes the height h (in feet) of the stone after "t" seconds is given below.
h=-16t^2+64t+40
How many seconds after the stone is thrown would it reach for the first time 100 feet in height?
======================
h=-16t^2+64t+40 = 100
Solve for t.
There might be 2 solution, ascending and descending.

Question 993286: e can spend $500 for the trip. Round trip train fare is$138 and he expects to spend ab average of $60 per week while he is there. What is the maximum amount of time anthony stay ib California before his money runs out? Answer by Theo(5548) (Show Source): You can put this solution on YOUR website! total money available is 500 round trip train fare is 138. subtract 138 from 500 and he has 362 left. he expects to spend an average of 60 per week while he's there. 362 / 60 = 6 weeks. that's the maximum he can stay there. he'll have 2 dollars left when he returns. Question 993332: if a father is 20 years older than his son. What is the sum of their ages seven years ago? Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! if a father is 20 years older than his son. What is the sum of their ages seven years ago? --------------- I don't know. Question 993339: A man The day on which you Rupees had a habit of spending less (Ex. 18 Table 18 Rs.) Once it is spending Rs 63 for 5 consecutive days So tell me, He was 5 dates on what? Answer by ikleyn(988) (Show Source): You can put this solution on YOUR website! . I am placing here the exact formulation and then the solution. -------------------------------------------------------------------------- Mr. X had a habit of spending money according to dates. For example, if date was 19 he was spending 19 rupees, and if date was 15 he was spending 15 rupees. One night he calculated total spending of 5 consecutive days - Monday to Friday, and he found that he spent 63 rupees in 5 days. So, identify the dates. (Assume that everyday spending is integer number of rupees). ------------------------------------------------------------------------- Answer. There is only one solution: 28 and 29 of February of a leap-year and 1, 2, and 3 of March. (28 + 29 + 1 + 2 + 3 = 63). Solution If these days would be inside one month, then the dates are (x-2), (x-1), x, (x+1) and (x+2), where x is the date in the middle of 5 days. Then the sum must be multiple of 5, since (x-2) + (x-1) + x + (x+1) + (x+2) = 5x. But the integer 63 is not multiple of 5. Contradiction. Hence, the dates are partly the end of some month and the beginning of the next month. Then, it is easy to check that the dates 28, 29, 1, 2 and 3 satisfy the condition 28 + 29 + 1 + 2 + 3 = 63. Next, it is easy to check that there is no other solution. The solution of this problem was placed in this forum one week ago http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.992162.html . The solution for the similar problem was placed in the lesson Spending money according to dates in this site couple of weeks ago. Question 993343: A stone is thrown vertically upward from the roof of a building. The formula that describes the height h (in feet) of the stone after "t" seconds is given below. How many seconds after the stone is thrown would it reach for the first time 100 feet in height? Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! No formula is given. Question 993318: A student buys some pens for 400$. If the cost of each pens is 9\$ less, he can buy 9 pens more from the same money. Find the number of pens
You can put this solution on YOUR website!
Let = the number of pens

Multiply both sides by

The student bought 16 pens
-------------------------
check:

OK

Question 993249: Jonathan has 1 3/4 hours to practice guitar. If he spends 1/8 hour on each song, how many songs can Jonathan practice? For how many minutes does he practice each song?
You can put this solution on YOUR website!
You cannot compare apples and oranges. You have to bring them to a common measure.
So, the easy part: 1/8 means that 1 hour is 8/8. And 3/4, we multiply both sides times 2 and we get 6/8. Now we add, he has 8/8+6/8= 14/8 hours to practice guitar. Now, (14/8)/(1/8)= 14/8 x 8/1= (14 x 8)/(8 x 1)= 112/8= 14 songs is what he can practice.
Next, an hour has 60 minutes: (60/1) x (1/8)= (60 x 1)/(1 x 8)= 60/8= 7.5 minutes per song.
Note: Practice the rules for fractions.

Question 993185: In the first season a baseball stadium sells 126 tickets than the second season. In the third season, it sells 262 fewer than the second season. If the stadium sells 3632 tickets collectively, how many tickets were sold each season?
You can put this solution on YOUR website!
Hi there,
Assume the second season = 'x'
First season = x + 126
Third season = x - 262
x + (x + 126) + (x - 262) = 3632
x + x + 126 + x - 262 = 3632
Collect like terms
3x = 3632 - 126 + 262
3x = 3768
x = 1256
First season - 1382 tickets sold
Second season - 1256 tickets sold.
Third season - 994 tickets sold.
Hope this helps :-)

Question 993161: To get an A in her math course, Tina needs, the average of five tests to be at least 90. Her current test scores are 80, 91, 85, and 84. What range of scores on the fifth test would get her an A in the course? Please explain how I need to solve this and set the problem up
You can put this solution on YOUR website!
.
.

.
So for average of 90 over 5 tests:
.

.

.

.

.

.

.
ANSWER: She must score at least 110
on the fifth test to average 90 over the 5 tests.

Question 993130: last month you used 125 minutes and your bill was 37.50. this month you used 175 minutes. how much will my bill be this month