Tutors Answer Your Questions about Linear Equations And Systems Word Problems (FREE)
Question 295619: a company has an income of $100,000 before paying taxes and a bonus. the bonus B is to be 20% of the income after deducting income taxes T but before deducting the bonus. so
B=0.20(100,000-T)
because the bonus is a deductible expense, the amount of income tax T at a 40% rate is 40% of the income after deducting the bonus. so
T=0.40(100,000-B)
solve the system algebraically to find the bonus and the amount of tax
Click here to see answer by richwmiller(9144)   |
Question 295619: a company has an income of $100,000 before paying taxes and a bonus. the bonus B is to be 20% of the income after deducting income taxes T but before deducting the bonus. so
B=0.20(100,000-T)
because the bonus is a deductible expense, the amount of income tax T at a 40% rate is 40% of the income after deducting the bonus. so
T=0.40(100,000-B)
solve the system algebraically to find the bonus and the amount of tax
Click here to see answer by palanisamy(496) |
Question 295649: Any help not good at these problems
J. Bond and E. Blofeld are driving speedboats in opposite directions after a failed attempt by the latter to blow up the world with a nuclear bomb. Mr. Bond’s boat is going 25 MPH faster than Mr. Blofeld’s. After 3 hours they are 500 miles apart. How fast was each of them going?
Eric
Click here to see answer by richwmiller(9144) |
Question 295651: . Solve using the five-step problem-solving process. Show all steps necessary to arrive at your solution. Round your answer to 2 decimal places when necessary.
The area of a circle is 28 square meters. What is its circumference? (Use п = 3.14. Hint: Area of Circle: A = пr2 and Circumference of Circle: C = 2пr)
Click here to see answer by richwmiller(9144) |
Question 295935: Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line with a slope of 5.9.
With 54 gallons of fuel in its tank, the airplane has a weight of 2418.6 pounds. What is the weight of the plane with 26 gallons of fuel in its tank?
Click here to see answer by nerdybill(7008)  |
Question 295942: Please can anyone help me understand this word problem.
A manufacturer makes three different drinks. Drink 1 contains 20% juice and 80% carbonated water. Drink 2 contains 50% juice and 50% carbonated water. Drink 3 contains 80% juice and 20% carbonated water. The manufacturer currently has available 100 liters of juice and 120 liters of carbonated water. Drink 1 sells for $1 per liter, Drink 2 sells for $2 per liter, and Drink 3 sells for $3.80 per liter. How many liters of each should the manufacturer make to maximize revenues?
A) 96.7 liters of Drink 1, 60 liters of Drink 2, 70.0 liters of Drink 3
B)66.0 liters of Drink 1, 20 liters of Drink 2, 83.3 liters of Drink 3
C)126.7 liters of Drink 1, 0 liters of Drink 2, 93.3 liters of Drink 3
D)106.7liters of Drink 1, 40 liters of Drink 2, 80.0 liters of drink 3
This is what I got so far, but no understand what to do next.
Drink 1: .2j .8c and sells for 1
Drink 2: .5j .5c and sells for 2
Drink 3: .8j .2c and sells for 3.8
Maximize: z = x1 + 2x2 + 3.8x3
Subject to: .2x1 + .5x2 + .8x3 = 100
.8x1 + .5x2 + .2x3 = 120
Thanks to anyone who can help.
Click here to see answer by Theo(3504)  |
Question 295958: During the school fair, the student council sold lemonade at 25 cents for each 260 ml.glass. Altogether they sold 420 glasses. The lemonade was purchased at a cost of 60 cents per liter. How much profit did the student council make?
Click here to see answer by richwmiller(9144) |
Question 295971: I need to develop a linear system of two equations that will show how many servings of each vegetable will give me the recommended daily allowance of calcuim and iron....
my known items are:
10 oz pkg of broccoli has 159 mg of calcium and 2.3 mg iron
1/2 c of corn has 3.3 mg of calcium and .3 mg of iron
the RDA of calcium is 1000 mg and RDA of iron is 18 mg
i know that i will need 6 servings of broccoli and 16 servings of corn to get the RDA of each nutrient....but how would I write this out and be able to solve it?
i have gotten as far as x + y = 1018 mg
6x + 16y = 1026 mg but now i am stuck...HELP!
Click here to see answer by scott8148(6628)  |
Question 296151: You sell tickets for admission to your school play and collect a total of $104. Admission prices are $6 for adults and $4 for children. You sold 21 tickets. How many adult tickets and how many children tickets did you sell?
Click here to see answer by mananth(12270)  |
Question 296242: Point of no return. A plane flying the 3458-mile trip from New York City to London has a 50-mph tailwind. The flight's point of no return is the point at which the flight time required to return to New York is the same as the time required to continue to London. If the speed of the plane in still air is 360-mph, how far is New York from the point of no return?
Please help I have tried and tried to figure this problem out and can't.
Click here to see answer by richwmiller(9144) |
Question 296318: A rectangular field is to be enclosed with a fence. One side of the field is against an existing fence, so that no fence is needed on that side. If material for the fence cost $2 per foot for the two ends and $4 per foot for the side parallel to the existing fence, find the dimensions of the field of the largest area that can be enclosed for 1,000.
Thanks in Advance
Click here to see answer by ankor@dixie-net.com(15746)  |
Question 296379: Could you please help me on this word problem:
The Rocket Coaster has 15 cars, some that hold 4 people and some that hold 6 people. There is room for 72 people altogether. How many 4-passenger cars are there? How many 6 passenger cars are there?
Click here to see answer by stanbon(57967) |
Question 296339: 4. Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
A plane flying the 3020-mile trip from City A to City B has a 60-mph tailwind. The flight's point of no return is the point at which the flight time required to return to City A is the same as the time required to continue to City B. If the speed of the plane in still air is 430 mph, how far from City A is the point of no return? Round your answer to the nearest mile.
Click here to see answer by ankor@dixie-net.com(15746) |
Question 296468: THE DIFFERENCE OF TWO NUMBERS IS 88. THE SECOND NUMBER IS 20% OF THE FIRST NUMBER. WHAT ARE THE NUMBERS? TRANSLATE INTO A PAIR OF LINEAR EQUATIONS IN TWO VARIABLES AND SOLVE USING ELIMINATION OR SUBSTITUTION METHOD.
Click here to see answer by stanbon(57967) |
Question 296477: a plane flying the 3020-mile round trip fron city A to city B has a 60 mph tailwind. the flight's point of no return is the point at which the flight time required to return to city A is the same as the time required to continue to city B.if the speed of the plane in still air is 430 mph, how far from city A is the point of no return? I need to translate this into a pair linear equation in two variables and am stuck. can you help? I can work the problem once i have it in an equation. Thanks.
Click here to see answer by scott8148(6628) |
Question 296477: a plane flying the 3020-mile round trip fron city A to city B has a 60 mph tailwind. the flight's point of no return is the point at which the flight time required to return to city A is the same as the time required to continue to city B.if the speed of the plane in still air is 430 mph, how far from city A is the point of no return? I need to translate this into a pair linear equation in two variables and am stuck. can you help? I can work the problem once i have it in an equation. Thanks.
Click here to see answer by richwmiller(9144) |
Question 296474: a plane flying the 3020-mile trip from city A to city B has a 60mph tailwind. the flight's point of no return is the point at which the flight time required to return to city A is the same time as the time required to continue to city B. If the speed of the plane in still air is 430mph, how far from city A is the point of no return ? I need to translate this problem into a pair linear equation in two variables and I am stuck. Where do I begin? I can work the problem out once I have the equation. can you help?
Click here to see answer by richwmiller(9144) |
Question 296493: A plane flying the 3020-mile trip from City A to City B has a 60-mph tailwind. The flight's point of no return is the point at which the flight time required to return to City A is the same as the time required to continue to City B. If the speed of the plane in still air is 430 mph, how far from City A is the point of no return? Round your answer to the nearest mile.
Click here to see answer by richwmiller(9144) |
Question 296571: The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. What are the length and the width?
Click here to see answer by mananth(12270) |
Question 296606: Kelly works in a store that pays $5.90 per hour and as a waitress that pays $12 an hour. Last week she worked 9 more hours at the store than she did as a waitress and earned $159.75. How many hours did she work at each job?
Click here to see answer by richwmiller(9144) |
Question 296952: Please help me solve this equation:
identify the system of equations.
4x + 3y = 10
12x + 9y = 28
a) inconsistent - no solutions
b) independent - one solution
c) dependent - many solution
identify the system of equations.
3x + 2y = 7
-4x - 3y = 10
a) inconsistent - no solutions
b) independent - one solution
c) dependent - many solutions
Click here to see answer by dabanfield(803) |
Question 297056: man drives car at 80 miles per hour for 30 minutes. His wife tries to meet up with him going 90 miles per hour. How long will she have to drive to catch him? and how far from their house will she finnally meet up with him?
Click here to see answer by richwmiller(9144) |
Question 297333: The Carmike 14 Theatre charges $8 for an adult ticket and $4.50 for a child’s ticket. On a particular Friday night, the entire 950 seat theater was full. The total ticket receipts for the evening were $6462.50. How many of each type of ticket were sold?
Click here to see answer by richwmiller(9144) |
Question 297592: Determine which, if any, of the three statements are equivalent.
I) If the rain is falling, then the ladybugs do not crawl on the plants.
II) If the ladybugs do not crawl on the plants, then the rain is not falling.
III) If the rain is falling, then the ladybugs crawl on the plants.
a). I, II, and III are equivalent
b). I and II are equivalent
c). II and III are equivalent
d). I and III are equivalent
e). None are equivalent
Click here to see answer by richwmiller(9144) |
Question 298684: Can some help solve this story problem, please and thank you!
Tropical Pools sells an aboveground model for p dollars each.
The monthly revenue for this model is given by the formula:
R (p) -0.08p^2 + 300p (the formula)
a) Factor out the price on the right-hand side of the formula.
b) Write a formula D (p) for the monthly demand.
c) Find D (3000).
Click here to see answer by stanbon(57967) |
Question 298724: THe formula b=26a is used in New England to estimate the minimum furnace output, b, in BTU's for a modern house with a square feet of flooring
a) determine the minimum furnace output for a 1700 ft(squared) modern house
b) solve formula for a
Click here to see answer by nerdybill(7008) |
Question 298866: A horse trainer is putting up a fence for the horses she train. The trainer has purchased enough wood to build 1500 feet of fence. To give the horses room to run, the trainer wants the length of the fence to be at least twice its width.
Which ordered pair gives a length and a width that satisfies the conditions above?
a)(600,200)
b)(600,175)
c)(500,275)
d)(500,250)
Thank you :)
Click here to see answer by user_dude2008(1861) |
Question 299123: Anew car worth 18,000 is depreciating by value by $3,000 per year. X should represent the # of years since the cars purchase, write an expression for the cars value using the given information.
original value depreciates by (/ - x +)
by 3,000 per year for x years
Click here to see answer by checkley77(12569) |
Question 299228: Tom Johnson and Melissa Acino started driving at the same time in different cars from Oklahoma City. They both traveld south on Route 35. Whem melissa covered a distance of 150 miles, tom had only covered a distance of 122 miles. If melissa avveraged 14 miles per hour faster than tom, find the average speed of each car.
Click here to see answer by mananth(12270) |
Question 300001: For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent." Then, answer the question about its solutions.
First,
L1:y= 2x-1
L2: -2x+y=-1
The system of equations is:
inconsistent, consistent dependent, consistent independent
This means:
a unique solution ( , )
infinitely many solutions
No solution
Second,
L1: y= 3/2x - 2
L2:y= 3/2 x
The system of equations is:
inconsistent, consistent dependent, consistent independent
This means:
a unique solution ( , )
infinitely many solutions
No solution
Third,
L1:y= -1/2x-2
L2 y= x+1
The system of equations is:
inconsistent, consistent dependent, consistent independent
This means:
a unique solution ( , )
infinitely many solutions
No solution
Click here to see answer by stanbon(57967) |
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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
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