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

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Question 994744: A local theatre sold 500 seats for an upcoming play. Ticket prices for adults are $62.00 and ticket prices for children are$32.00. If the theatre made $26,140.00 for the show, how many adult and children attended? Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! A local theatre sold 500 seats for an upcoming play. Ticket prices for adults are$62.00 and ticket prices for children are $32.00. If the theatre made$26,140.00 for the show, how many adult and children attended?
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Quantity:: a + c = 500 tickets
Value:: 62a + 32c = 26140
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Modify for elimination::
31a + 31c = 31*500
31a + 16c = 13070
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Subtract and solve for "c":
15c = 2430
c = 162 (# of child tickets sold)
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a = 500-162 = 338 (# of adult tickets sold)
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Cheers,
Stan H.
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Question 994762:
Frank purchased tools that totaled $24.80. If he had to pay a 6% sales tax, how much did Frank have to pay in total? Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! Frank purchased tools that totaled$24.80. If he had to pay a 6% sales tax, how much did Frank have to pay in total?
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Ans: 1.06*24.80 = $26.29 ------- Cheers, Stan H. ---------------- Question 994724: You have$15.50 to spend on party food. Gum drops are $3 per pound, yogurt-covered peanuts are$2.50 per pound, and cashews are $4.50 per pound. Question 2: If you buy 0.5 pound of gum drops and an equal weight of yogurt-covered peanuts and cashews, how much can you afford to buy? Answer by josgarithmetic(13975) (Show Source): You can put this solution on YOUR website! x, the amount pounds each of yogurt covered peanuts and the cashews to buy Question 994617: Please identify if the equations are consistent, inconsistent, dependent or independent. 2x- 9y = 7 5x + 6y = 8 Answer by Alan3354(47455) (Show Source): Question 994565: The manager of a restaurant earns$2.25 more each hour than the host of the restaurant. Write an equation that relates the amount "h" that the host earns each hour when the manager earns $11.50 each hour. Answer by fractalier(2141) (Show Source): You can put this solution on YOUR website! Call m the manager's salary. Then m = h + 2.25 If m = 11.50, then$11.50 = h + $2.25 Question 994672: in order to control certain type of diseases,it is necessary to use 23 litres of chemical A and 34 litres of chemical B.The dealer can order commercial spray,I each container which hold 5 litres of chemical A and 2 litres of chemical B and commercial spray II,each container which hold 2 litres of chemical A and 7 litres of chemical B.How many container of each type of commercial spray should be used to get the exact proportion of chemical needed ? Answer by josgarithmetic(13975) (Show Source): You can put this solution on YOUR website! VARIABLES x, count of sprayer I y, count of sprayer II ACCOUNT FOR CHEMICAL VOLUMES OF A and B A: 5x+2y=23 B: 2x+7y=34 Solve the system of the two equations for x and y. Question 994670: ten years ago a father was six time as old as his son. After 10 years, he will be twice as old as his son. determine their present ages. Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! ten years ago a father was six time as old as his son. After 10 years, he will be twice as old as his son. determine their present ages. ------- Equations: f-10 = 6(s-10) f+10 = 2(s+10) ------------ Rearrange:: f - 6s = -50 f - 2s = 10 -------------- Subtract and solve for "s":: 4s = 40 s = 10 yrs (son's age now) --- Solve for "f": f - 2s = 10 f-20 = 10 f = 30 yrs (father's age now) --------------- Cheers, Stan H. ---------- Question 994631: How many packs of DVD's can you buy with 225 dollars of one pack costs 17 dollars? Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! Divide 225 by 17. Round down. Question 994616: Please identify if the equations are consistent, inconsistent, dependent or independent. 2x – 3y = -5 2x + 4y = 10 Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! Independent. Question 994615: please identify if the equations are consistent, inconsistent, dependent or independent. x + 4y = -10 2x – 3y = 13 Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! Independent. Question 994628: Solve for x if (⅔)Ax + 10 = 6B . Answer by Fombitz(25151) (Show Source): Question 994594: Jon has to pay$7.00 admission for the skating rink and $1.50 per hour to rent roller blades. How many hours can he skate for$19
Found 2 solutions by macston, solver91311:
You can put this solution on YOUR website!
.
H=Hours he an skate; T=total cost
T=$7.00+($1.50/hr)H
T-$7.00=($1.50/hr)H
(T-$7.00)/($1.50/hr)=H
.
For T=$19: ($19.00-$7.00)/($1.50/hr)=H
$12.00/($1.50/hr)=H
8hrs=H
.
ANSWER: Jon can skate 8 hours for $19.00. Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! Subtract 7 from 19 and then divide the result by a buck and a half. John My calculator said it, I believe it, that settles it Question 994546: The sum of a two-digit number is 13. If the number is multiplied by 6, the result is 456. Write and solve a system of equations and find the number. Found 4 solutions by solver91311, josgarithmetic, macston, Alan3354: Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! In the first place, I think you meant to say that the sum of the digits of a two-digit number is 13. Otherwise I would have to ask you "the sum of a two-digit number and what?" since addition is a binary operation. Be that as it may, you don't need a system of equations to solve this problem. You only need one equation, namely: John My calculator said it, I believe it, that settles it Answer by josgarithmetic(13975) (Show Source): You can put this solution on YOUR website! "Sum of a two-digit number is 13", means the two digit number IS 13. You would then already know the number and not solve for it. If the sum OF THE DIGITS of a two-digit number is 13, then this is very different. t, the tens digit u, the units or ones digit Number is 10t+u. t+u=13. The "next" part of the description means, (10t+u)*6=456. Solve this system: . Answer by macston(4006) (Show Source): You can put this solution on YOUR website! . x=the number 6x=456 x=76 ANSWER: The number is 76. . Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! If the number is multiplied by 6, the result is 456. Write and solve a system of equations and find the number. --------- 456/6 = 76 Question 994403: i spent 3/8 of my money. i found out that i have 24pesos left. how much did i have at first? Answer by Cromlix(3061) (Show Source): You can put this solution on YOUR website! Hi there, 3/8 of your money = 24 pesos 8 x 24/3 = the money you had first. = 64 pesos. Hope this helps :-) Question 994419: A local convenience store owner spent$10 on 144 pencils to resell at the store. What is the equation of the store's profit if each pencil sells for $0.50? graph the equation Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! A local convenience store owner spent$10 on 144 pencils to resell at the store. What is the equation of the store's profit if each pencil sells for $0.50? graph the equation. ------ Profit = Revenue - Cost ------- P = 0.50*144 - 10 ---- P = 72 - 10 --- Profit =$62.00
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Cheers,
Stan H.

Question 994149: If a car wash charges $5 but after you have stayed for 10 minutes they charge$.40 for every minute continuing. What would be an equation for this problem? Please answer fast, thank you
Found 2 solutions by MathTherapy, rothauserc:
You can put this solution on YOUR website!
If a car wash charges $5 but after you have stayed for 10 minutes they charge$.40 for every minute continuing. What would be an equation for this problem? Please answer fast, thank you
, with "C" being the total cost and "m" being the total number of minutes spent there



You can put this solution on YOUR website!
let m be total minutes at car wash
1) if m < 10 then
cost = $5 2) if m > 10 then cost =$5 + ((m - 10) * 0.40)

Question 994184: A group of retailers will buy 104 televisions from a wholesaler if the price is $500 and 144 if the price is$450. The wholesaler is willing to supply 68 if the price is $450 and 148 if the price is$540. Assuming the resulting supply and demand functions are linear, find the equilibrium point for the market.
(q, p) =

You can put this solution on YOUR website!

Use the two-point form of the equation of a line to write the supply and demand functions.

where and are the coordinates of the given points.

Then solve the 2X2 stem for the point of intersection of the two lines.

John

My calculator said it, I believe it, that settles it

Question 994147: Ocean Bike Rental Shop charges $17 +$8 an hour for renting a bike. Benny paid $73 to rent a bike. How many hours did he paid to have the bike checked out? Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! Ocean Bike Rental Shop charges$17 + $8 an hour for renting a bike. Benny paid$73 to rent a bike. How many hours did he pay to have the bike checked out?
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Solve::
73 = 17 + 8x
---
8x = 56
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x = 7 hrs
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Cheers,
Stan H.

Question 994125: AB makes 50 units in 15 days. A makes 50 units in 15. In how many days B makes 50 units?
Found 2 solutions by ikleyn, solver91311:
You can put this solution on YOUR website!
.

You can put this solution on YOUR website!

Zero

John

My calculator said it, I believe it, that settles it

Question 994075: Students in a painting class must pay an art supplies fee. On the first day of class, the instructor collected a total of $27 in fees from several students. On the second day she collected$45 more from some other students, and on the third day she collected another $63 from some more students. (A) what is the most the art supplies fee could cost per student? (B) use your answer in part (a) to determine how many students paid the art supplies fee each day 1st day 2nd day 3rd day Answer by Boreal(1464) (Show Source): You can put this solution on YOUR website! It has to be the largest factor of$27, and that is $9. Conceivably, it could be$3, or even $1, but the question is the most the fee could be. Therefore, 3 students paid the first day, 5 the second, and 7 on the third. Question 993908: One hundred tickets are sold for a movie at the cost of$10 each. Some tickets have cash prizes as a part of a promotional campaign. There is one prize of $50, three prizes of$25, and five prizes of $20. What is the expected gain if you buy one ticket? Answer by Theo(5548) (Show Source): You can put this solution on YOUR website! one hundred tickets are sold at 10 dollars apiece. 1 prize at 50 3 prices at 25 5 prizes at 20. probability of winning 50 is 1/100. probability of winning 25 is 3/100. probability of winning 20 is 5/100. your expected gain is -10 + (1/100 * 50) + (3/100 * 25) + (5/100 * 20). that is equal to -7.75 dollars. your are expected to lose 7.75 dollars for every 10 dollar ticket you buy. does this make sense? let's see. suppose you bought all 100 tickets. your cost would be 10 * 100 = 1000 dollars. you would win 1 * 50 + 3 * 25 + 5 * 20 = 50 + 75 + 100 = 225 dollars. you lost 1000 dollars and you gained 225 dollars, so your net gain is -775 dollars. a negative net gain is a positive net loss. you lost 775 dollars. take the 775 dollars and divide it by 100 and you lost an average of 7.75 on each ticket. your net loss is an average of 7.75 on each ticket. your net gain is an average of -7.75 on each ticket. i believe they were asking for expected gain on one ticket. that answer is -7.75. Question 993946: Brenda's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 4 adult tickets and 3 child tickets for a total of$75. The school took in $25 on the second day by selling 1 adult ticket and 2 child tickets. What is the price each of one adult ticket and one child ticket? Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! Brenda's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 4 adult tickets and 3 child tickets for a total of$75. The school took in $25 on the second day by selling 1 adult ticket and 2 child tickets. What is the price each of one adult ticket and one child ticket? ---- 1st Day:: 4a + 3c = 75 2nd Day:: a + 2c = 25 --------------------- Modify for elimination: 4a + 3c = 75 4a + 8c = 100 --- Subtract and solve for "c":: 5c = 25 c = 5 (Price of a child ticket) -------- Solve for "a":: a + 2c = 25 a + 10 = 25 a = 15 (Price of an adult ticket) ------------ Cheers, Stan H. ---------- Question 993965: linear equation a customer walks into a post office to purchase stamps. she purchased a total of 47 stamps some of the stamps are 49 cents stamps and some 33 cent stamps how many 49 cents stamps and how many 33 cents stamps did she purchase if the total cost of all the stamps was 20.31 Found 2 solutions by lwsshak3, stanbon: Answer by lwsshak3(11500) (Show Source): You can put this solution on YOUR website! a customer walks into a post office to purchase stamps. she purchased a total of 47 stamps some of the stamps are 49 cents stamps and some 33 cent stamps how many 49 cents stamps and how many 33 cents stamps did she purchase if the total cost of all the stamps was 20.31 let x=number of 49 cents stamps customer bought 47-x =number of 33 cents stamps customer bought . 49x+.33(47-x)=20.31 .49x+15.51-.33x=20.31 .16x=14.80 x=30 47-x=17 number of 49 cents stamps customer bought=30 number of 33 cents stamps customer bought=47 Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! a customer walks into a post office to purchase stamps. she purchased a total of 47 stamps some of the stamps are 49 cents stamps and some 33 cent stamps how many 49 cents stamps and how many 33 cents stamps did she purchase if the total cost of all the stamps was 20.31 ----------------------- Quantity:: t + n = 47 stamps Value:: : 33t+49n = 2031 cents ---------------------------------- Modify for elimination: 49t + 49n = 49*47 33t + 49n = 2031 -------- Subtract and solve for "t":: 16t = 272 t = 17 (# of 33 cent stamps purchased) ----------- Cheers, Stan H. ----------- Question 993949: The school that Jenny goes to is selling tickets to a fall musical. On the first day of ticket sales the school sold 7 senior citizen tickets and 14 student tickets for a total of$175. The school took in $215 on the second day by selling 12 senior citizen tickets and 7 student tickets. What is the price each of one senior citizen ticket and one student ticket? Answer by Boreal(1464) (Show Source): You can put this solution on YOUR website! x=SR y=student 7x+14y=175 12x+7y=215 ====== 7x+14y=175 -24x-14y=-430, multiplying it by (-2). Now add -17x=- 255 x=$15 SR
105+14y=175
14y=70
y=$5 student ====== check with second 12*15=$180
7*5=$35. They add to$215

Question 993948: Rob and Amy each improved their yards by planting daylilies and ornamental grass. They bought their supplies from the same store. Rob spent $104 on 12 daylilies and 8 bunches of ornamental grass. Amy spent$22 on 6 daylilies and 1 bunch of ornamental grass. What is the cost of one daylily and the cost of one bunch of ornamental grass?
You can put this solution on YOUR website!
daylily cost=x
grass cost=y
12x+8y=104
6x+y=22
y=22-6x
12x+8(22-6x)=104 by substitution
12x+176-48x=104
-36x=-72
x=$2 for daylily Substitute into first 24+8y=104 8y=80 y=$10 for ornamental grass
========
check with second
6(2)+10=$22 Question 993950: Stefan and Bill each improved their yards by planting hostas and shrubs. They bought their supplies from the same store. Stefan spent$117 on 7 hostas and 10 shrubs. Bill spent $108 on 8 hostas and 5 shrubs. What is the cost of one hosta and the cost of one shrub? Answer by Boreal(1464) (Show Source): You can put this solution on YOUR website! x=hostas cost y=shrubs cost 7x+10y=117 8x+5y=108 ====== 7x+10y=117 -16x-10y=-216, multiplying the bottom by (-2) -9x=-99 x=11 substitute into first 77+10y=117 y=4 ===== check with second 88+20=108 hosts are$11
shrubs are $4 Question 993935: Caroline has a rectangular vegetable garden that measures 4 m x 6 m . she wants to divide the garden into three equal sections to plant three different vegetables . what is the area of each section ? Answer by fractalier(2141) (Show Source): You can put this solution on YOUR website! Since the original area can be found by multiplying length times width, we get 4 m x 6 m = 24 m^2 as the total area. We want to divide this by three and get 24 / 3 = 8 m^2 for each smaller section. Question 993917: Answer by Alan3354(47455) (Show Source): Question 993866: If m-p=3 and mp=-1 the what is the value of (m+p)^2? Answer by Alan3354(47455) (Show Source): You can put this solution on YOUR website! If m-p=3 and mp=-1 the what is the value of (m+p)^2? ---------- m-p = 3 --> m = p+3 --- m*p = -1 (p+3)*p = -1  Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=5 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.381966011250105, -2.61803398874989. Here's your graph: --------- p = -0.381966011250105 m = 2.618034 --> (m+p)^2 = 5 ---------------- p = -2.61803398874989 Same. Question 993741: Hi,I need help on this question. I've tried to solve the problem but I keep getting stuck. This is the question: A corporate team-building event costs$2 for every attendee. How many attendees can there be, at most, if the budget for the corporate team-building event is $20? Answer by Theo(5548) (Show Source): You can put this solution on YOUR website! the budget is 20 doll;ars. the cost for each attendee is 2 dollars. 20 / 2 = 10 the maximum number of attendees is 10. if 10 attend, then the total cost is 10 * 2 = 20. it can be less than 10, but it can't be more than 10, because more than 10 will cost more than 20 dollars total. for example, 11 * 2 = 22 which is greater than 20. Question 993754: Isabel would be paid about what you paid$8 per hour plus tips average tip is 4.50 per table if you work 25 hours a week how many tables would she have to serve to make $362 for the week Answer by josmiceli(13716) (Show Source): You can put this solution on YOUR website! Let = number of tables served She has to serve 36 tables Question 993827: there were twenty one adults in line at a movie theater that is three times the number of children in line how many children were in line Answer by addingup(248) (Show Source): You can put this solution on YOUR website! 21/3= 7 children Question 993730: Jason weighs 200 pounds. He wants to weigh at most 175 pounds. if he loses 2 pounds per week on his new diet, how long must he stay on his diet to reach his goal? Write an equation or inequality to solve the word problem Answer by addingup(248) (Show Source): You can put this solution on YOUR website! 200-2x= 175 -2x= -25 x= -25/-2 negative and negative is positive: x= 12.5 weeks Question 993608: Sue is planning to haveI rectangular flower Garden next and will enclose it with 54 feet of fencing. She decides that the length of her garden will be 1 foot less then three times the width. What will be the dimensions of her garden Answer by Cromlix(3061) (Show Source): You can put this solution on YOUR website! Hi there, Make width = 'x' Length = 3x - 1 Perimeter = 54 feet Perimeter = 2 x Width + 2 x Length 54 = 2(x) + 2(3x - 1) 54 = 2x + 6x - 2 Collect like terms. 2x + 6x = 54 + 2 8x = 56 x = 7 Width = 7 feet Length = 20 feet. Hope this helps :-) Question 993457: For what value of B does the function F(x)=-3x^2+Bx-4 have only 1 x-intercept. Find all possible values of B and leave your answer in exact form. Answer by ikleyn(988) (Show Source): You can put this solution on YOUR website! . For what value of B does the function F(x) = have only 1 x-intercept. Find all possible values of B and leave your answer in exact form. ------------------------------------------------------------------------- It may happen if and only if two real roots of the quadratic polynomial F(x) = merge into one real root of multiplicity 2. It is the case when the plot of the quadratic polynomial touches x-axis. In turn, a necessary and a sufficient condition for it is vanishing the discriminant of the polynomial, which is - 4*(-3)*(-4) = 0, or = 16*3. It gives B = and/or B = - . At these values of B F(x) = or F(x) = correspondingly. Answer. B = and/or B = - .  Plots (in red) and (in green) Question 993564: Danny and Mary want to go to a concert next weekend. the tickets will cost$70. After Mary gives Danny all the money she has in her wallet. Danny must come up with $5 less than twice Mary's contribution to pay for the tickets. How much will each contribute for the tickets? Answer by addingup(248) (Show Source): You can put this solution on YOUR website! Mary gave her money to Danny. We'll call her money x Danny must come up with$5 less than 2x, this is, 2x-5. Finally:
x+2x-5= 70 add 5 on both sides
x+2x= 75 Add x on left
3x= 75 Divide both sides by 3
x= 25 This is how much money Mary gave Danny. So, Danny must come up with:
25*2-5= 50-5= 45 This is the amount Danny must come up with. Let's see if it's true:
25 Mary + 45 Danny = 25+45= 70 We've got the right answer.

Question 993565: Sue is planning to have a rectangular flower garden next and will enclose is with 54 feet of fencing. She decides that the length of her garden will be one foot less than times the width. What will be the dimensions of her garden?
You can put this solution on YOUR website!
You say: "She decides that the length of her garden will be one foot less than times the width"
Than how many times the width??

Question 993530: there are 30 people on a field trip. the students total twice as many as adults students tickets coast $4 and adult tickets coast$8. write an equation that represents the number of people on the trip