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

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Question 290396: a. Suppose a market research company finds that at a price of p = $20, they would sell x = 42 tiles each month. If they lower the price to p = $10, then more people would purchase the tile, and they can expect to sell x = 52 tiles in a month’s time. Find the equation of the line for the demand equation. Write your answer in the form p = mx + b. Hint: Write an equation using two points in the form (x,p).
Click here to see answer by stanbon(57211)

Question 290191: how do i solve this problem algebraically?
two airplanes left the same airport traveling in opposite directions. if one airplane averages 400 mph and the other 250 mph, how many hours willl it take for the distance between them be 1625 miles?
i know the answer is 2.5 hours but i dont know how to get there.
Click here to see answer by rentot12(1)

Question 290510: Write equation for the line. Use slope-intercept form if possible.
through (5, -6) and (0,-8).
A) y = -2/5x -8 B) y = 11/8x -8 C) y = 2/5x -8 D) y = -11/8x - 8
This is what I got.
y = 2/5x + b
Do not know how to solve for b. Thanks for your time.

Click here to see answer by richwmiller(9135)

Question 290772: A discount store sold plastic cups for $3.50 each and ceramic cups for 4.00 each. if 400 cups were sold for a total of 1,458, how many cups of each were sold? What was the dollar value of each type sold?

Click here to see answer by richwmiller(9135)

Question 290774: Lashonna is a buyer for Plough. She can purchase 100 pounds of chemicals for 97. At this same rate, how mmuch would 2,000 pounds of the chemical cost?
Click here to see answer by Deina(147)

Question 290924: Hello all, I am struggling with the following problem. I know it is probably really easy and im just not understanding something, but I keep getting stuck on how to express the variable for calculating the amount of each coin and there $ value in each equation. Any help will be great.
A jar contains 100 coins made up of 50 cent coins and 20 cent coins. How many coins are there if the total value of the coins is $38.00. Solve algebraically.
a) Express this problem as a system of two equations. Define variables correctly.
b) Solve system of equations simultaneously.
Thanks, -Nick.
Click here to see answer by stanbon(57211)

Question 290964: Is (-1,2), (1,2), (-2,4, (2,4) a linear equation. I put no since the domain does not equal one range number
Click here to see answer by stanbon(57211)

Question 290964: Is (-1,2), (1,2), (-2,4, (2,4) a linear equation. I put no since the domain does not equal one range number
Click here to see answer by richwmiller(9135)

Question 290984: Trucking company needs to move 21 tons of gravel. You have 8 qualified drivers in the company and two types of trucks. One type can haul 5 tons. The other can haul 3 tons. An insurance requirement specifies that 5-ton trucks must have two drivers in the cab. 3 ton trucks only need one driver. Set up two equations for this problem. One to represent the drivers and one to represent the amount of tonnage hauled. Let X represent the number of 5-ton trucks and y the number of 3 ton trucks. Solve for x and y that will satisfy both equations. That is, determine how many of each size of truck should be used to move the gravel in one trip, using all available drivers.
Click here to see answer by richwmiller(9135)

Question 290970: The sum of the ages of Joe and Jim is 90. Six years from now, Joe will be twice Jim's age. Find Joe's present age.
Click here to see answer by Deina(147)

Question 291210: The sum of two numbers is 16. The difference of two numbers is 6. Let X respresent the larger number and Y respresent the smaller number. Help me Set up Linear system. Please
Click here to see answer by checkley77(12569)

Question 291332: how much of a 40% solution would you need to combine with a 15% solution to get 30 ounces of 20% solution

Click here to see answer by richwmiller(9135)

Question 291751: Starting at 8 A.M. determine the
number of times in the next 24 hours for which the hour
and minute hands on a clock coincide.
Click here to see answer by richwmiller(9135)

Question 290625: A school sold 200 tickets to a play. Ticket prices were $8 per adult and $5 per child. If the total sales for the tickets came to $1414, how many children's tickets were sold?
Click here to see answer by nyc_function(2733)

Question 292428: Rita recieved a $70 gift card for a coffee store. She used it in buying some coffe that cost $8.58 per pound. After buying the coffe, she had $35.68 left on her card. How many pounds of coffe did she buy?
Click here to see answer by richwmiller(9135)

Question 292559: Problem: The difference between two positive integers is 36. One integer is three times as great as the other. Find the integer.
So far, I made an equation of x+2=36+3(x).
The problem is that when I check my work 19=87, so my equation can't be right.
I need some help with turning this problem into an equation!
Click here to see answer by jim_thompson5910(28476)

Question 292873: A boat traveled 336 miles downstream and back. The trip downstream took 12 hours. The trip back
took 14 hours. What is the speed of the boat in still water? What is the speed of the current?
12)
Click here to see answer by ankor@dixie-net.com(15622)

Question 293013: Jon has 1121 pointsw in his math class. He must have 88% of the 1400 points possible by the end of the term to recieve credit for the class. What is the minimum number of additional points he must earn by the end of the term to receive credit for the class?
What I've tried:
88% of 1400=88/100*1400=1232-1121=111 points
The problem: 111+1121=1232, not 1400.
Where am I going wrong?
Click here to see answer by richwmiller(9135)

Question 292999: At a gourmet coffee store, the price of Hawaiian coffee is $8.50 per pound, and the price of Colombian coffee is $7.70 per pound.
Find how many pounds of each kind should be mixed to obtain 200 pounds of a mixture of the two kinds of coffee that will sell at $8.30 per pound.
Click here to see answer by richwmiller(9135)

Question 293158: 2. As you are leaving the community, you notice another new community just down the street. Because you are in the area, you decide to inquire about it.
a. The sales representative here tells you they also have two floor plans available, but they only have 38 homes still for sale. Write an equation that illustrates the situation. Use x and y to denote floor plan one and floor plan two respectively.
X+y=38
b. The representative tells you that floor plan one sells for $175,000 and floor plan two sells for $200,000. She also mentions that all the available houses combined are worth $7,200,000. Write an equation that illustrates this situation. Use the same variables you used in Part a.
c. Use elimination to determine how many houses are available in each floor plan. Explain how you arrived at your answer.

Click here to see answer by richwmiller(9135)

Question 293231: Rachel is a saleswomen.She is paid a base salary of $1800 a month pluse a 4% commision on the sales she makes.What was her sales amount last month if she earned a total of $2671.24?
Click here to see answer by stanbon(57211)

Question 293277: The sum of two numbers is less than or equal to 18. The second number is 8 less than the first. What are the possible values for the first of the two numbers?

Click here to see answer by Edwin McCravy(8879)

Question 293300: thanks for the help in advance trying to help a friend.
Yellow trucking company for a round trip is 30$ and .10$ a mile after 250 miles
Gray trucking company for a round trip is 20$ and .10$ a mile.
I know to graph this you use Y=mx+b
But i keep coming up with answers that are wrong because i am not sure were to start on graphing it or if i am doing something wrong.
Click here to see answer by stanbon(57211)

Question 293431: I missed one class due to illness and now I am very lost. I think I need help determining which formulas to use for this word problem. I have plotted a few different ways and not sure if it makes sense. Here is the question:
Irvin's parents allow him to use the family car provided he pay for the gas, which averages $1.60 per gallon. The car averages 20 miles per gallon. To help Irvin earn gas money, this parents pay him $10 a week to do chores. Determine and then plot a weekly savings equation for Irvin that represents earnings minus money spent on gas. Write a physical interpretation for both intercepts of the savings equation.
I have tried having x=miles and y=allowance. I got a slope of 12.5 (which was cents per gallon of gas) I would appreciate any help on this.
Thank you so much.

Click here to see answer by richwmiller(9135)

Question 293438: Tickets for a show cost $6.00 for adults and $4.50 for children. 400 tickets were sold for a total of $2100. How many adult tickets and how many childrens tickets were sold?
Click here to see answer by unlockmath(1599)

Question 293644: Martina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A has no initial fee but charges $0.90 for every mile driven.
Company B charges an initial fee of $55 and an additional $0.40 for every mile driven.

For what mileages will Company A charge more than Company B?
Use m for the number of miles driven, and solve your inequality for m.
Click here to see answer by brucewill(101)

Question 293754: A manufacturer wants to enlarge an existing facility such that the total floor area is 1.6 times that of the current facility. The floor area of the current facility is rectangular 250 ft by 160 ft. The manufacturer wants to increase each dimension by the same amount.
Can someone walk me step by step on this problem?
Click here to see answer by richwmiller(9135)

Question 293823: There are two fruit stalls that are located on separate areas in the park. At the end of the day, the first stall sold 25 apples and 10 oranges for a total of 610 pesos. The second stall sold 13 apples and 18 oranges for a total of 506 pesos. Find how much one orange cost
Click here to see answer by richwmiller(9135)

Question 294233: dustin and lydia order 3 ham sandwiches and 2 chicken sandwiches and pay $2.85. Kylie and Rupert order 6 ham sandwiches and 1 chicken sandwich and pay $3.90. Formulate a system of equations that can be used to find the prices of ham sandwiches and chicken sandwiches.
Click here to see answer by stanbon(57211)

Question 294449: the length of a rectangle is 1 ft less than 3 times the width. the area of the rectangle is 310 ft. what are the dimensions of the rectangle. When i did the question i got w = 77.75 but when substituted in the equations that didn't make sense the equations i used were L*W=310 and 3W-1=L
Click here to see answer by richwmiller(9135)

Question 294605: Taylor and Susan each have a box that is in the shape of a cube. The edges Taylor's box are each x cm high. The edges of Susan's box are 4 cm longer than on Taylor's cube. What binomial expansion represents the volume of Susan's box?
Click here to see answer by Earlsdon(6287)

Question 294766: Please help m solve the following: 8y=7y, solve for y....Thank you
Click here to see answer by richwmiller(9135)

Question 294733: The cost in millins of dollars for a company to manufacture x thousand automobiles is given by the function C(x)= 4x^2-16x+32. Find the number of automobiles that must be produced to minimize the cost

Tried to factor out the four then simpliy. Stuck. Help!
Click here to see answer by jim_thompson5910(28476)

Question 294806: A person wants to set up an internet plan. Plan A costs 30 dollars per month and .10 per minute. Plan B costs 20 dollars per month and .15 per minute. Write a system of equations and how many minutes of use result in the same charge for both plans? What would the charge be?
Click here to see answer by rfer(12644)

Question 294785: ``Solve by using the elimination method.2r-9s=-109r+2s=40 What is the solution of the system ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A) the solution is_______(type an ordered pair. use integers or fractions for any numbers in the expression.)B)There are infinitely number of solutions.C) There is no solution.
Please help me answe this. I am not coming up with the right answer!
Click here to see answer by ankor@dixie-net.com(15622)

Question 294737: A book case is to be constructed. The height is 4 feet longer than the length of a shelf. If 20 feet of lumber is available for the entire unit,except the back, find the length and height of the unit.
The book case to be constructed consist of 4 horizontal lines and
the two vertical lines. I am stuck on a formula to use for this.

Click here to see answer by scott8148(6628)

Question 295109: At a movie theater, tickets cost 9.50 for adults and 6.50 for children . A group of 7 moviegoers pays a total of 54.50. How many adults and how many children are in the group.
Click here to see answer by rfer(12644)

Question 295135: I have a word problem that says, "Determine whether an outfitter leading a backpacking trip would find it more cost effective to make a one time bulk purchase at a buyers club with membership fees or purchase the same goods at a conventional supermarket." I have to develop an algebraic equation for each option and then graph it. I believe the equations should be in the form "y=mx+b". I chose trail mix as an appropriate real world item to price compare, and found Sam's club membership fees to be 35.00, and Sam's club trail mix to cost 7.48 for a 48oz bag. I went to Walmart supercenter to compare and their biggest bag is 28 oz for 4.98. So the two equations I have are y=(4.98/28)x+o for walmart and y=(7.98/48)x+35 for Sam's club. Is this correct? I'm not sure if I'm factoring in the membership fee correctly. Thank you for taking the time to help me.
Click here to see answer by Theo(3458)

Question 295297: If 6 times a number is added to -7, the result is equal to 13 times the number. Find the number.
Now the instructions say to let x represent the number...

so i think this is how it goes but i'm unsure of the rest:
6(x-7)=13x
Click here to see answer by richwmiller(9135)

Question 295386: A helicopter blade is 2.75 m long and is rotating at 420 rpm. What is the linear velocity of the tip of the blade?
Click here to see answer by Fombitz(13828)

Question 295520: How much pure water must be mixed with 6 pints of 60% developer to produce a mixture that is 19% developer?
I just cannot come up with equations for this problem.
I have x representing the pure water and y representing the 60% solution.
The only equation I can come up with is:
x + 6y = .19
Please help me solve this problem. Thank you!
Click here to see answer by richwmiller(9135)

Question 295618: 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)
a. graph the equations on the same coordinate system.
b. what happens to the supply as the price increases? ( would like hint)
c. What happens to the demand as the price increases? (would like hint)
d. The price at which supply and demand are equal is called the equilibrium price. What is the equilibrium price? (Hint if possible, otherwise, this would be where the lines would intersect each other correct?
Thank you for your time and patience. The examples in textbook are garbage and do not relate to the following question.
Click here to see answer by richwmiller(9135)

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