Tutors Answer Your Questions about Miscellaneous Word Problems (FREE)
Question 1208467: A movie hall sold tickets to one of its shows in two denominations, $11 and $7. A fourth of all those who bought a ticket also spent $4 each on refreshments at the movie hall. If the total collections from tickets and refreshments for the show was $124, how many $7 tickets were sold? Note: The number of $11 tickets sold is different from the number of $7 tickets sold.
Click here to see answer by math_tutor2020(3816)  |
Question 1208468: A candy manufacturer decided to decrease the weight of each candy bar, while retaining the price. By how many cents did the per kilogram cost of candy change after the reduction in weight?
Statement 1: The weight of each piece of candy bar reduced by 9 grams.
Statement 2: The weight of each piece of candy bar reduced by 9%.
Click here to see answer by ikleyn(52775)  |
Question 1208468: A candy manufacturer decided to decrease the weight of each candy bar, while retaining the price. By how many cents did the per kilogram cost of candy change after the reduction in weight?
Statement 1: The weight of each piece of candy bar reduced by 9 grams.
Statement 2: The weight of each piece of candy bar reduced by 9%.
Click here to see answer by Edwin McCravy(20054)  |
Question 1208465: The basic one-way air fare for a child aged between 3 and 10 years costs half the regular basic fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult?
Click here to see answer by ikleyn(52775) |
Question 1208465: The basic one-way air fare for a child aged between 3 and 10 years costs half the regular basic fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult?
Click here to see answer by greenestamps(13198)  |
Question 1208481: Hi
John and Lester were cycling towards the finish line. 15km from the end John passed Lester. John reached the end 45 minutes earlier than Lester who was still 9km from the end. What was John's speed after overtaking Lester.
Click here to see answer by ikleyn(52775) |
Question 1208494: From the top of a fire tower, a forest ranger sees his partner on the ground at an angle of depression of 40º. If the tower is 45 feet in height, how far is the partner from the base of the tower, to the nearest tenth of a foot?
Click here to see answer by ikleyn(52775) |
Question 1208623: Hi
A delivery van was travelling at an average speed of 50km per hour for the first 20 minutes. The driver took a wrong turn and realised that he would be late by 10 minutes. He then increased his speed to 75km per hour. When he arrived he was early by 6 minutes. How far did he travel.
Click here to see answer by ikleyn(52775) |
Question 1208653: The period T, in seconds, of a pendulum of length L, in feet, may be approximated using the formula
T = 2•pi•sqrt{L/32}
For part B, express your answer both as a square root and as a decimal.
A. Solve the given formula for L.
B. Find the period T of a pendulum whose length is 8 inches.
For part B, 8 inches must be converted to feet before substituting into the given formula.
You say?
Click here to see answer by Shin123(626)  |
Question 1208652: The final velocity v of an object in feet per second (noted aa ft/sec) after it slides down a frictionless inclined plane of height h feet is given by
v = sqrt{64h + (v_0)^2}, where v_0 is the initial velocity (in ft/sec) of the object.
A. Solve the given formula for h.
B. What is the final velocity v of an object that slides down a frictionless inclined plane of height 4 feet? Assume that the initial velocity is 0.
Click here to see answer by Shin123(626) |
Question 1208650: An electric circuit contains three resistors connected in parallel. If the resistance of each is R_1, R_2, ams R_3 ohms, respectively, their combined resistance R is given by the formula
1/R = (1/R_1) + (1/R_2) + (1/R_3)
A. Express R as a rational expression.
B. Evaluate R for R_1 = 5 ohms, R_2 = 4 ohms, and R_3 = 10 ohms
Let me see.
I think for A, I need to solve for R. If so, I will use a for R_1, b for R_2, and c for R_3 for easy cell phone typing.
1/R = 1/a + 1/b + 1/c
After much effort on paper, solving for R leads me to
R = (abc)/(bc + ac + ab).
Is this correct? If so, part B is just plug and chug.
You say?
Click here to see answer by Shin123(626) |
Question 1208651: A shell station stores it's gasoline in underground tanks that are right circular cylinders lying on their sides. The volume V of gasoline in the tank (in gallons) is given by the formula
V = (40h^2)(sqrt{(96/h) - 0.607}, where h is the height of the gasoline (in inches) as measured on a depth stick.
A. Can h be isolated for this formula?
B. If h = 1 inch, how many gallons of gasoline are in the tank?
Let me see.
I say part A is not possible. There’s no general algebraic formula to solve for h directly. You say?
For part B, I simply let h = 1 in the formula and evaluate for V.
You say?
Click here to see answer by Shin123(626) |
Question 1208651: A shell station stores it's gasoline in underground tanks that are right circular cylinders lying on their sides. The volume V of gasoline in the tank (in gallons) is given by the formula
V = (40h^2)(sqrt{(96/h) - 0.607}, where h is the height of the gasoline (in inches) as measured on a depth stick.
A. Can h be isolated for this formula?
B. If h = 1 inch, how many gallons of gasoline are in the tank?
Let me see.
I say part A is not possible. There’s no general algebraic formula to solve for h directly. You say?
For part B, I simply let h = 1 in the formula and evaluate for V.
You say?
Click here to see answer by Alan3354(69443)  |
Question 1208419: Hi
Mrs Johnson and her 2 sons Bernard and raymond shared a sum of money. The ratio received by Mrs Johnson to that received by Bernard was 5 to 2 . The ratio of money received by Bernard to that received by Raymond was 3 to 4 . After Mrs Johnson gave 20% of her share to Raymond and Bernard donated 1/3 of his share to charity. Raymond then had $4270 more than Bernard.
What was the sum of money shared by the three of them.
Click here to see answer by MathTherapy(10551)  |
Question 1208690: At exactly 12 o'clock noon the hour hand of a clock begins to move at four times its normal speed, and the minute hand begins to move backward at two-thirds its normal speed. When the two hands next coincide, what will be the correct time?
Click here to see answer by ikleyn(52775) |
Question 1208698: A builder of tract homes reduced the price of a model by 15%. If the new price is $425,000, what was its original price? How much can be saved by purchasing the model?
All throughout my time with math (all my life), setting up the right equation using the given data in word problems has been a major personal frustration.
Here is my effort, which is wrong.
Price of model = x
Reduced by 15% = x - 0.15
Equate to new price:
x - 0.15 = 425,000
This is obviously and miserably wrong.
I know there is a general equation or formula for finding the original price of items. However, let's say you are taking a test and came across this question. You don't know if there is a general equation or formula that can be used to find the original price. How would you approach this problem to find the correct answer?
Click here to see answer by ikleyn(52775) |
Question 1208697: Going into the final exam, which will count as two tests, Jack has test scores 80, 83, 71, 61, and 95. What score does Jack need on the final in order to have an average score of 80?
My setup, which leads to the wrong answer, is this:
(80 + 83 + 71 + 61 + 95 + 2x)/6 = 80
Here, 2x = 2 tests. This is my understanding. I am wrong.
A. Why is my setup wrong?
B. If you were taking a test and came across this word problem, how would you break it down leading to the right equation or setup?
Click here to see answer by josgarithmetic(39616) |
Question 1208697: Going into the final exam, which will count as two tests, Jack has test scores 80, 83, 71, 61, and 95. What score does Jack need on the final in order to have an average score of 80?
My setup, which leads to the wrong answer, is this:
(80 + 83 + 71 + 61 + 95 + 2x)/6 = 80
Here, 2x = 2 tests. This is my understanding. I am wrong.
A. Why is my setup wrong?
B. If you were taking a test and came across this word problem, how would you break it down leading to the right equation or setup?
Click here to see answer by greenestamps(13198) |
Question 1208697: Going into the final exam, which will count as two tests, Jack has test scores 80, 83, 71, 61, and 95. What score does Jack need on the final in order to have an average score of 80?
My setup, which leads to the wrong answer, is this:
(80 + 83 + 71 + 61 + 95 + 2x)/6 = 80
Here, 2x = 2 tests. This is my understanding. I am wrong.
A. Why is my setup wrong?
B. If you were taking a test and came across this word problem, how would you break it down leading to the right equation or setup?
Click here to see answer by math_tutor2020(3816) |
Question 1208696: Rita grossed $435 one week working 52 hours. Rita's employer pays time-and-a-half for all hours over 40 hours. With this information, can you determine Rita's regular salary wage?
Textbook Solution
1. We are looking for hourly wage.
2. Let x = regular hourly wage for Rita's
3. Set up a table
Table
Regular Hours = 40
Hourly wage = x
Salary = 40x
Overtime hours = 12
Hourly wage = 1.5x
Salary = 12(1.5x) = 18x
The correct equation is 40x + 12(1.5)x = 435
My equation is 40x + 12(1.5) = 435
Question
Why must 12 hours be multiplied by 1.5x instead of simply 1.5? Understand? You say?
Click here to see answer by josgarithmetic(39616) |
Question 1208696: Rita grossed $435 one week working 52 hours. Rita's employer pays time-and-a-half for all hours over 40 hours. With this information, can you determine Rita's regular salary wage?
Textbook Solution
1. We are looking for hourly wage.
2. Let x = regular hourly wage for Rita's
3. Set up a table
Table
Regular Hours = 40
Hourly wage = x
Salary = 40x
Overtime hours = 12
Hourly wage = 1.5x
Salary = 12(1.5x) = 18x
The correct equation is 40x + 12(1.5)x = 435
My equation is 40x + 12(1.5) = 435
Question
Why must 12 hours be multiplied by 1.5x instead of simply 1.5? Understand? You say?
Click here to see answer by greenestamps(13198) |
Question 1208716: Judy and Tom agreed to share the cost of an $18 pizza based on how much each ate. If Tom ate 2/3 the amount that Judy ate, how much should each pay?
HINT GIVEN IN THE TEXTBOOK:
[ Some pizza may be left over.]
This hint tells me nothing.
Let me see.
The cost of the pizza is $18.
Judy ate x part of the pizza.
Tom ate (2/3)x part of the pizza.
My equation is (2/3)x + x = 18.
You say?
Click here to see answer by ikleyn(52775) |
Question 1208714: The manager of the Coral Theatre wants to know if the majority of its patrons are adults or children. One day in July, 5200 tickets were sold, and the receipts totaled $29.96. The adult admission is $7.50, and the children's admission is $4.50. How many adult patrons were there?
In this word problem, I see a system of equations in two variables.
Let a = adult
Let c = children
My two equations are as follows:
a + c = 5200
7.50a + 4.50b = 29.96
Is my system of equations correct?
Click here to see answer by josgarithmetic(39616) |
Question 1208714: The manager of the Coral Theatre wants to know if the majority of its patrons are adults or children. One day in July, 5200 tickets were sold, and the receipts totaled $29.96. The adult admission is $7.50, and the children's admission is $4.50. How many adult patrons were there?
In this word problem, I see a system of equations in two variables.
Let a = adult
Let c = children
My two equations are as follows:
a + c = 5200
7.50a + 4.50b = 29.96
Is my system of equations correct?
Click here to see answer by ikleyn(52775) |
Question 1208714: The manager of the Coral Theatre wants to know if the majority of its patrons are adults or children. One day in July, 5200 tickets were sold, and the receipts totaled $29.96. The adult admission is $7.50, and the children's admission is $4.50. How many adult patrons were there?
In this word problem, I see a system of equations in two variables.
Let a = adult
Let c = children
My two equations are as follows:
a + c = 5200
7.50a + 4.50b = 29.96
Is my system of equations correct?
Click here to see answer by timofer(104) |
Question 1208713: A college book store marks up the price that it pays the publisher for a book by 35%. If the selling price of a book is $92.00, how much did the bookstore pay for this book?
Let me see.
Let x = money the store paid for the book
The store sold the book for $92 after marking up the price they paid for the book by 35%.
This is where I start guessing my way to the equation I hope is correct to solve the problem. After more than 15 minutes with this question, I gave up.
This is my equation based on my understanding:
0.35x = 92.00
Obviously, I am wrong because the correct answer is $68.15.
What equation setup leads to $68.15?
Click here to see answer by josgarithmetic(39616) |
Question 1208707: What is the maximum number of bottles, each of diameter 9 cm, that can be packed into a box with a square base measuring 990 cm by 990 cm? The diagram below shows the closest packing method.
https://ibb.co/x1WDp3H
Click here to see answer by ikleyn(52775) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690
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