Questions on Word Problems: Linear Equations And Systems Word Problems answered by real tutors!

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Question 198193: Suppose you have a hot dog stand, and when you charge $1 per hot dog you sell 75 hot dogs. But when you raise your price to $2 you only sell 50 dogs. Write an equation for the number of hot dogs you sell as a function of the price you charge. Use "H" for number of Hot dogs, and "P" for the price you charge for your hot dogs. You can assume the function is linear.
Click here to see answer by stanbon(57347)

Question 198209: Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 50 cups. But when you raise your price to $2 you only sell 25 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear.
Click here to see answer by josmiceli(9678)

Question 198216: The sum of two numbers is 33. The greater number is 3 more than the lesser number . Find the numbers.
Click here to see answer by solver91311(16885)

Question 198216: The sum of two numbers is 33. The greater number is 3 more than the lesser number . Find the numbers.
Click here to see answer by stanbon(57347)

Question 198213: The royalties for the high school play are 250 dollars.Tickets to the play cost 5dollars for students and 8 dollars for nonstudent tickets. What linear inequality describes the number of student and nonstudent tickets that need to be sold so that the drama class can pay the royalties
Click here to see answer by josmiceli(9678)

Question 198309: A driver notices that after driving 100 miles there are 12.8 gallons of fuel left in her car's tank. After driving 300 miles she notices that there are only 6.4 gallons left in the tank.
A) Determine a linear function that will give the number of gallons left in the tank as a function of the number of miles driven.
B)Based on this model how much fuel does the tank hold?
Click here to see answer by stanbon(57347)

Question 198308: The value of a certain car decreases at the rate of 300 dollars each month after being prucahsed new. Suppose that the car is worth $17,000 when it is 2 years old.
A) Determine a linear function that will give the value of the car as a function of months since being purchased.
B)Use this model to determine the value of the car after 4 years.
Click here to see answer by Madgamer107(9)

Question 198307: The boiling point of water at sea level is 100 degrees Celsius. The boiling point decreases 3.5 degrees for every 1 Kilometer increase in altitude.
A) Determine a linear function that will give the boiling point of water as a function of altitude.

B) Use this model to determine the boiling point of water at 2 Kilometers above sea level.

Click here to see answer by Alan3354(30993)

Question 198533: 1. A number consist of 2 digits whose is 11. If the digits are interchanged,the value of the number decrease by 20sq.m. Find the length and breadth of the room.
2. If the numerator of a fraction is decreased by 1 its value becomes 2/3, but if the denominator is increased by 5, the value becomes 1/2 . what is the fraction.
Click here to see answer by edjones(7569)

Question 198555: Investing her bonus. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25% then how much did she invest at each rate?
Click here to see answer by checkley75(3666)

Question 198713: Mr. Greene has 8.5 in by 11 in cardboard sheets. As a class project, Mr. Greene asked each of his students to amke an open-top box under these conditions:
I. Each box must be made by cutting small squares from each corner of a cardboard sheet.
II. The box must have a volume of 48 in^3
III. The amount of cardboard waste must be minimized.
What is the appropriate side length for the small squares that would be cut from the cardboard sheet?
Click here to see answer by ankor@dixie-net.com(15652)

Question 198785: One number is 11 more than twice another number. If the sum of the numbers is twice their difference, find the numbers.
Click here to see answer by edjones(7569)

Question 198956: solve and graph this system of equations
3x - 5y = -9
5x - 6y = -8
Click here to see answer by jim_thompson5910(28595)

Question 199002: y=2(x-4)^2-2
a. sketch the graph
b. Label the intercepts and vertex
c. Give exact values and show your work
Click here to see answer by stanbon(57347)

Question 199008: Solve for X by any method; Show work.
A. 0= 1/4x^2+2x

B. 0= 9x^2-64
C. 0= 6x^2+5x-4
Click here to see answer by stanbon(57347)

Question 199007: A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose a suitable rectangular coordinate system and find the equation of the parabola. Then calculate the height of the arch 10, 20 and 40 feet from the center. Provide a sketch representing the situation and be sure it is clearly labeled with coordinates.
Click here to see answer by ankor@dixie-net.com(15652)

Question 199108: The cost of 12 gallons of regular gasoline and 18 gallons of premium gasoline is $44.46. Premium costs $.22 more per gallon than regular. What is the cost per gallon of each type of gasoline?
Click here to see answer by checkley75(3666)

Question 199155: 2x < 7 + x
Click here to see answer by checkley75(3666)

Question 199306: Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as:
1. Integers
2. Rational numbers
3. Irrational numbers
Click here to see answer by rfer(12660)

Question 199416: Find an equation for which -3 and 4 are solutions.
I am having some concentration problems
Click here to see answer by rfer(12660)

Question 199415: I need to find a equation in which -3 and +4 are solutions.
I am really stumped
Click here to see answer by solver91311(16885)

Question 199414: I need to solve for the discriminate and determine the number of solution and classify it for the equation:
square root of 2x^2-4x-7sq root of 2-0
can you help me?
Click here to see answer by solver91311(16885)

Question 199357: The perimeter of a rectangle 36m. The width is 18 yd less than twice the length. Find the length and width of the rectangle.

Click here to see answer by checkley77(12569)

Question 199518:
Jacque earns $8.60 per hour (h). For overtime (each hour over 40 h) he earns $12.90 per h. If he works 55.5 h in a week, what pay should he receive?
Click here to see answer by vleith(2825)

Question 199530: Kristi jogged for 3/5 of an hour, swam for1/2 of an hour, and rode her bicycle for 3/4 of an hour. How long dis she exercise?
Click here to see answer by jim_thompson5910(28595)

Question 199611: Problem: The Jurassic Zoo charges $28.00 for each adult admission and $12.00 for each child. The total bill for 454 people from a school trip was $3860.00. How many adults and how many children went to the zoo? how would set this problem up useing polynomials
Click here to see answer by vleith(2825)

Question 199623: An investigator uses forms A, B, C in filling out reports. He uses form B five times as often as form A, and he uses form C three times as often as form B.
If the total number of all forms used in a month equals 735, how many times was form B used?
Click here to see answer by rfer(12660)

Question 199742: Explain in your own words, using the definition of probability why: a) the probability of an event that cannot occur is 0; b) the probability of an event that must occur is 1.
Click here to see answer by RAY100(1637)

Question 199839: The second of two numbers is 5 more than twice the first. The sum of the numbers is 44. How do you solve this problem in an equation?
Click here to see answer by Alan3354(30993)

Question 200148: How do you solve for this equation?
Click here to see answer by rfer(12660)

Question 200360: A jazz concert brought in $191,000 on the sale of 7400 tickets, if tickets were sold for $20 and $30 each, how many of each type of ticket were sold?
Click here to see answer by nerdybill(6958)

Question 200326: The cross-country teams of East and West run against each other twice each fall. At the first meet, East's score was two thirds of West's score. At the second meet East's score increased by seven points and West's score decreased by seven points. In the second meet West's score was three less than East's score. How many points did Each team score in each meet?
Click here to see answer by ankor@dixie-net.com(15652)

Question 200464: Using a 30% window cleaner solution, and a 60% window cleaner solution, how many liters of each will be needed to create 80L of 45% window cleaner solution?
Click here to see answer by Alan3354(30993)

Question 200485: A jeweller has bars of 18 carat gold and 12 carat gold. how much of each must be melted toghter to obtain a bar of 16 carat gold, weighting 120 gm? Given pure gold is 24 carat.
Click here to see answer by ankor@dixie-net.com(15652)

Question 200406: A boat took 5 hours to travel 60 kilometers up a river against a current. The return trip took 3 hours .Find the speed of the boat in still water and the speed of the current.

Solve the linear system
x-2/3 + y+1/5 = 2
x+2/7 - y+5/3 = -2

Click here to see answer by ankor@dixie-net.com(15652)

Question 200496: Venture capital. Henry invested $12,000 in a new
restaurant. When the restaurant was sold two years
later, he received $27,000. Find his average annual
return by solving the equation 12,000(1 + r)2 =
27,000.
Click here to see answer by rfer(12660)

Question 200643: Alex, Stuart and Ali recieve an average of $12 per week in pocket money. Alex recieves $2 more than Stuart, but $5 less than Ali. How much does each one recieve?
Could you please help me answer this question

Click here to see answer by rfer(12660)

Question 200671: Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, HCF). When graphed, the function gives a line with a slope of 1.75 . See the figure below.
If the monthly bill for 17 HCF is$22.76 , what is the monthly bill for 21 HCF?

Click here to see answer by rfer(12660)

Question 200805: Gita is one third as old as her mother.Twelve years hence she
will be half as old as her mother.What is the present age of
Gita and her mother?

Click here to see answer by josmiceli(9678)

Question 200913: 13). A purse contains one rupee.50 paise and 25paise coins in the
ratio 2:3:4.If the total value of the coins is Rs 90,find the number
coins in each denominations.
14). The digit at tens place of a two digit number is four times the
digit at unit place.If the sum of this number and the number
formed by reversing the digits is 55.Find the number.
*15).Three prizes are to be given in a quiz contest.The value of the
second prize is three fourth of the value of the first prize and
four third of the third prize.If the total value of the three prizes
is Rs 222.Find the prize value of each prize.
16).The numerator of a fraction is 5 less than the denominator.If 3
is added to both the numerator and the denominator,the new
fraction is 2/3.Find the fraction.
* 17).A man is 40 years old and his son is 12 years old.
(i) How many years ago was the man’s age eight times the age
of his son?
(ii) How many years hence will the age of the man be three
times the age of his son?
18) . The perimeter of a triangle measures 49cm.The one side is
7cm longer than the other and 5cm shorter than the third .
Find the length of each side
*19). A field can be ploughed in 14 days.If 20 hectares of land is
ploughed more daily,the work will be finished in 10 days.Find
the area of the land which can be ploughed daily.Also find the
area of the field.

1). Find the value of 2x3- 3x2 + x – 1 if x = -2.
2). If x= 1,y= 2, z= -1,find the value of each of the following
expressions.
2xy4 – 15x2y + z (ii) x3 + y3+ z3 – 3xyz
(iii)x3 –y3+ z3+ 3xyz (iv) 4xy2 – 3yz2 + 4x2z
3). Add the following expressions
(i)x3, ,-3x3,2x3,-4x3 (ii)2a2- 3ab,5a2 + 4ab
(iii) a2+ 2ab + b2,a2 – 2ab + b2,a2- b2
(iv) 18a – 10b,-2a + 12b,-10a + 6b
(v) 2x2 - 4x- 3,5x-6x2+ 2,6x-3 +5x2
4). Subtract
(i)4a +3b from 2a + 2b – 4 (ii) x2 + y2 from 5x2 + 3y2 + 2
(iii) 10a2 -5a from -10a -6a2
(iv) 6x3 – 7x2 + 5x – 3 from 4 – 5x + 6x2 – 8x3
(v) x2y -4xy2+ 4xy from 2x2y + 3xy2-xy
5). From the sum of 4x2 -6x + 3 and -4x2 -7x + 5 subtract 3x2-8x + 6.
6). What should be added to 5x2 + 6x -3 to get 3x + 2?
7). Multiply
(i) 9x2y and 2y2x2 (ii) -4/3ab and 3/2 a2c
(iii) x3(x2y + y2x) (iv) -8y( 2xy + 3y2)
(v) 3/5xy⌊1/10 x - 4/7 y⌋ (vi) xyz(4y2 + 9x2)
8.Simplify
i) p^2 (p^2 - q^2 ) + q^2 (p^2 - q^2 )
ii)a(b-c) - b(c –a) – c(a – b)
iii)xy^2 (4xy -2x^2 )- x^3 y( 1-2y)+ x^2 y(x- y^2 )
9. Find the products
i) (x + a)( x + b)
ii) (9x + 5y)(3x – 2y)
iii)(2x^2- 1)(4x^2+ 5x)
iv) (3x2 + 7y)(5x – 6y)
v)(3/5 xy+ 5/2 y^2 z)(2x-3yz)
10. Find the products and verify the results for x = 1 and y = -2
i)(7xy + 4y^2 )(3y^2+ 8x^2)
ii)(11y + 7x^2)(1/2 x^(3 )+ xy))
iii)(9x + 1/2 y^3 )(x^(3 )– y^3 )
11.Simplify
i)3x2 + 4x(3x – 4y) - 20 xy
ii)8ab x 2 b2 + 7a2b x (5y – 3x)
iii)1/5 ( 5x^(2 )+ 10y^2 )(x^2 – y^2 )
iv)(2x + y) (1 + 4x + 3y) - 6x (x + y)
v)(3y + 5x – 7)(x -1) – (y -2x + 3) (x + 4)
12.)Multiply
i) (x + y ) and (x2 – xy + y2) ii)(2a + 3) x 5a x (-a + 1)
iii)1/(2 ) m x (8m -6) x ( 4 – 12 m)
Click here to see answer by solver91311(16885)

Question 200947: please help me solve this problem:
a farmer and his son leave a barn at the same time and walk in opposite driections checking a fence line. the son walks at the speed of 3.5km/h and the farmer at 4.0km/h. how much time will have elapsed when the farmer and his son are 2.5km apart
Click here to see answer by nerdybill(6958)

Question 200990: If it takes Sally 4 hours to paint a house and John 6 hours to paint the same house, how long does it take them to paint the house together?
Click here to see answer by stanbon(57347)

Question 201090: i actually have two questions.
1) what is the answer to this question: the sum of two consecutive is -67
find the integers
2) the sum of two consecutive integers is 28
find the integers
how do i do this and write it out?
Click here to see answer by Alan3354(30993)

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