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Recent problems solved by 'stanbon'
stanbon answered: 57135 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 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54990..55019 , 55020..55049 , 55050..55079 , 55080..55109 , 55110..55139 , 55140..55169 , 55170..55199 , 55200..55229 , 55230..55259 , 55260..55289 , 55290..55319 , 55320..55349 , 55350..55379 , 55380..55409 , 55410..55439 , 55440..55469 , 55470..55499 , 55500..55529 , 55530..55559 , 55560..55589 , 55590..55619 , 55620..55649 , 55650..55679 , 55680..55709 , 55710..55739 , 55740..55769 , 55770..55799 , 55800..55829 , 55830..55859 , 55860..55889 , 55890..55919 , 55920..55949 , 55950..55979 , 55980..56009 , 56010..56039 , 56040..56069 , 56070..56099 , 56100..56129 , 56130..56159 , 56160..56189 , 56190..56219 , 56220..56249 , 56250..56279 , 56280..56309 , 56310..56339 , 56340..56369 , 56370..56399 , 56400..56429 , 56430..56459 , 56460..56489 , 56490..56519 , 56520..56549 , 56550..56579 , 56580..56609 , 56610..56639 , 56640..56669 , 56670..56699 , 56700..56729 , 56730..56759 , 56760..56789 , 56790..56819 , 56820..56849 , 56850..56879 , 56880..56909 , 56910..56939 , 56940..56969 , 56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149, >>NextPolynomials-and-rational-expressions/277813: Use three or more sentences to describe the process you would follow to completely factor the polynomial 3x6+24?
1 solutions
Answer 202212 by stanbon(57203)   on 2010-03-06 14:53:53 (Show Source):
You can put this solution on YOUR website!Use three or more sentences to describe the process you would follow to completely factor the polynomial 3x6+24?
----
Common Factor: 3
= 3(x^6 + 8)
---------
Rewrite:
= 3[(x^2)^3 + 2^3)
---
= 3[(x^2+2)(x^4 - 2x^2 + 4)
----------------------------------
Cheers,
Stan H.
|
Probability-and-statistics/277793: What is the t value for a 20% two-tailed test with degrees of freedom = 9
I do not just want an answer. I want to know step by step how to get the answer
1 solutions
Answer 202202 by stanbon(57203) on 2010-03-06 13:28:32 (Show Source):
You can put this solution on YOUR website!What is the t value for a 20% two-tailed test with degrees of freedom = 9
I do not just want an answer. I want to know step by step how to get the answer
------------
To get the answer you need a T-chart or a calculator that generates t-values,
such as a TI-84.
-------
Since the test is 2 tail, each tail has 10%
Check your T-chart for df=9 and left (or right) tail = 0.1000
---
Using a TI I get invT(0.9,9) = 1.3830
===================
Cheers,
Stan H.
|
Rational-functions/277792: Graph:
f(x) = -2x, x<=-2
f(x) = -3,-2
f(x) = 4x-6, x>1
On these types of problems I am used to being given an x-substitute, for example, graph problem one when x = 2, I would then sub in the number and solve. I am perplexed about how to do this without a substitute.
1 solutions
Answer 202201 by stanbon(57203) on 2010-03-06 13:23:41 (Show Source):
You can put this solution on YOUR website!
The second question was also messed up, it should have been
-3, when -2 < x <= 1
The way the problem is shown to me is
f(x) = {
and the three equations come within the single { which stretches to encompass all of them.
Graph:
f(x) = -2x, x<=-2
f(x) = -3, -2
f(x) = 4x-6, x>1
---------------------
So this is the graph of a semented function.
On the x-interval (-inf,-2] graph the line y = -2x
On the x-interval (-2,1} graph the line y = -3
On the x-interval (1,+inf) graph the line y = 4x-6
----------------------------------------------------------
To do each of these you need to determine two points
that are on each interval.
For example, on the (-inf,-2) interval you could have
(-5,10) and (-2,4)
Draw a line segment thru those points ending at (-2,4).
---
On the next interval you have points (-2,-3) and (1,-3)
Draw a line sement connecting those points.
------------------------
On the last interval you have points (1,-2) and arbitrary (4,10)
Draw a line segment that starts at (1,-2) and passes thru (4,10)
-----------------------------------------------------
Those three line segments comprise the graph of f(x)
======================================================
Cheers,
Stan H.
|
Surface-area/277789: The depth of a rectangular pool is 2 feet. The volume is 16 cubic feet. What is the area in square feet of the bootom of the pool?
1 solutions
Answer 202200 by stanbon(57203) on 2010-03-06 13:18:55 (Show Source):
You can put this solution on YOUR website!The depth of a rectangular pool is 2 feet. The volume is 16 cubic feet. What is the area in square feet of the bottom of the pool?
-------------------
Volume = Bh where B is the area of the base and h is the height.
------------------------
16 = B*2
B = 8 sq. ft.
============================
Cheers,
Stan H.
|
Triangles/276959: You have a 15' ladder leaning against a wall.
It just touches the edge of a 5'x5' shed in the corner.
How high up the wall does the ladder touch and
how far out from the wall does it rest on the ground?
|\
| \
| \
----
| | \
| | \
-------
I have tried using sin cos tan and a^2+b^2=c^2 but i can't seem to get it down to one variable that I can solve for or set them equal to.
1 solutions
Answer 202197 by stanbon(57203) on 2010-03-06 13:14:43 (Show Source):
You can put this solution on YOUR website!You have a 15' ladder leaning against a wall.
It just touches the edge of a 5'x5' shed in the corner.
How high up the wall does the ladder touch and
how far out from the wall does it rest on the ground?
-----------------
How high is the point where the ladder touches
the shed?
Cheers,
stan H.
|
Miscellaneous_Word_Problems/277740: To build a set of book shelves, a carpenter needs 30 identical boards, each 2 feet 7 inches long. For this type of wood, the lumber yard sells only 12 foot long boards. How many 12 foot long boards must the carpenter purchase?
A.6 B.7 C.8 D.9 E.More than 9
1 solutions
Answer 202169 by stanbon(57203) on 2010-03-06 09:52:23 (Show Source):
You can put this solution on YOUR website!To build a set of book shelves, a carpenter needs 30 identical boards, each 2 feet 7 inches long. For this type of wood, the lumber yard sells only 12 foot long boards. How many 12 foot long boards must the carpenter purchase?
------------
# of shelves he gets from each 12' board: 12'/2'7" = 144"/31" = 4.65
Round down to get 4 shelves from each 12' board
---
# of boards needed = 30/4 = 7 1/2
Round up to get 8 boards
-----
He will need 8 12' boards.
===============================
Cheers,
Stan H.
A.6 B.7 C.8 D.9 E.More than 9
|
Graphs/277749: Find the x- and y- intercepts
5x+y=15
1 solutions
Answer 202167 by stanbon(57203) on 2010-03-06 09:45:14 (Show Source):
You can put this solution on YOUR website!Find the x- and y- intercepts
5x+y=15
--------------
x-intercept?
Let y = 0 and solve for "x":
5x = 15
x = 3
--------------
y-intercept?
Let x = 0 and solve for "y":
y = 15
====================
Cheers,
Stan H.
|
Probability-and-statistics/277624: On a TV game show, the contestant is asked to select a
door and then is rewarded with the prize behind the door
selected. If the doors can be selected with equal probability,
what is the expected value of the selection if the
three doors have behind them a $40,000 foreign car, a $3
silly straw, and a $50 mathematics textbook?
1 solutions
Answer 202159 by stanbon(57203) on 2010-03-06 09:09:32 (Show Source):
You can put this solution on YOUR website!On a TV game show, the contestant is asked to select a
door and then is rewarded with the prize behind the door
selected. If the doors can be selected with equal probability,
what is the expected value of the selection if the
three doors have behind them a $40,000 foreign car, a $3
silly straw, and a $50 mathematics textbook?
-----
Random Number values: 40000,3,50
Probabilities: 1/3,1/3,1/3
---------------------------------
Expected Value: (1/3)(4053) = $1351
---------------------------------
Cheers,
Stan H.
|
Mixture_Word_Problems/277746: A company makes pigments used to color fabrics, plastics and paints. To ensure the finished product matches the customers expectations, pigments of varying strength are blended to obtain what is called a 100% strength commercial standard. The plant has 5000 pounds of Pigment Red 1 with strength of 123% of the standard, and they also have 17,890 pounds of Pigment Red 1 at 87% strength versus the same commercial standard.
Your boss wants to know how much of the 87% material is needed to blend with the 5000 pounds of the 123% material so that the final strength of the blended material is 100% strength. What do you tell him?
1 solutions
Answer 202158 by stanbon(57203) on 2010-03-06 09:05:56 (Show Source):
You can put this solution on YOUR website!A company makes pigments used to color fabrics, plastics and paints. To ensure the finished product matches the customers expectations, pigments of varying strength are blended to obtain what is called a 100% strength commercial standard.
The plant has 5000 pounds of Pigment Red 1 with strength of 123% of the standard, and they also have 17,890 pounds of Pigment Red 1 at 87% strength versus the same commercial standard.
Your boss wants to know how much of the 87% material is needed to blend with the 5000 pounds of the 123% material so that the final strength of the blended material is 100% strength. What do you tell him?
----------------------
Equation:
red + red = red
1.23x + 0.87(5000-x) = 1.00(5000)
Multiply thru by 100 to get:
123x + 87*5000 - 87x = 100*5000
36x = 13*5000
x = 1805.56 lbs (amt of 123% pigment needed for the mixture)
5000-1805.56 = 3194.44 lbs (amt of 87% pigment needed for the mixture)
===================================
Cheers,
Stan H.
|
Probability-and-statistics/277742: A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were
3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477
(a) Construct a 90 percent confidence interval for the true mean weight.
(b) What sample size would be necessary to estimate the true weight with an error of } 0.03 grams with 90 percent confidence?
(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.
1 solutions
Answer 202157 by stanbon(57203) on 2010-03-06 08:58:58 (Show Source):
You can put this solution on YOUR website!A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on
a very accurate scale. The results in grams were
3.087 3.131 3.3.241 3.270 3.353 3.400 3.411 3.437 3.477
(a) Construct a 90 percent confidence interval for the true mean weight.
E = z*sigma/sqrt(n)
E = 1.645*0.13199/sqrt(10)
E = 0.06866
--------------
x-bar = 3.3048
-----------------
90% CI = (3.3048-0.06866 , 3.3048+0.06866)
-----------------------------------------------
(b) What sample size would be necessary to estimate the true weight with an error of 0.03 grams with 90 percent confidence?
E = z*sigma/sqrt(n)
n = [z*sigma/E]^2
z* for 90% confidence = 1.645
sigma = 0.13199
E = 0.03
------------
n = [1.645*0.13199/0.03]^2 = 52.38
rounded up: n = 53
========================
(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.
Temperature; consistency of batches; machine tolerances
=========================
cheers,
Stan H.
|
Probability-and-statistics/277743: In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive.
(a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.
(b) Why is the normality assumption not a problem, despite the very small value of p?
1 solutions
Answer 202155 by stanbon(57203) on 2010-03-06 08:55:40 (Show Source):
You can put this solution on YOUR website!In 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive.
---
sample proportion = 1143/86991 = 0.013
standard error = E = 1.96sqrt(0.013*0.987/86991) = 0.000753
-------------------
(a) Construct a 95 percent confidence interval for the population proportion of positive drug tests.
95% CI: 0.013-0.000753 < p < 0.013+0.000753
95% CI: 0.01222 < p < 0.013753
====================================
(b) Why is the normality assumption not a problem, despite the very small value of p?
I'll leave that to you.
Cheers,
Stan H.
|
Probability-and-statistics/277629: The number of accidents that occur at the intersection
of Pine and Linden streets between 3 p.m. and
6 p.m. on Friday afternoons is 0, 1, 2, or 3, with probabilities
of 0.84, 0.13, 0.02, and 0.01, respectively.
Graph this probability distribution. What is the
expected value for the random variable given the
number of accidents?
1 solutions
Answer 202153 by stanbon(57203) on 2010-03-06 08:36:02 (Show Source):
You can put this solution on YOUR website! The number of accidents that occur at the intersection
of Pine and Linden streets between 3 p.m. and
6 p.m. on Friday afternoons is 0, 1, 2, or 3, with probabilities
of 0.84, 0.13, 0.02, and 0.01, respectively.
Graph this probability distribution. What is the
expected value for the random variable given the
number of accidents?
----------------------
The Graph.
Put 0,1,2,3 on the horizontal axis
Plot the probabilities as the y-values associated with 0,1,2,3
-------------------------------------------
E(x) = 0*0.84+1*0.13+2*0.02 + 3*0.01
= 0 + 0.13 + 0.04 + 0.03
= 0.21
=============
Cheers,
Stan H.
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Probability-and-statistics/277673: 1.Estimate the probability that a randomly selected person in the U.S. will be afflicted with
ashtma in 2003. Use this probability to estimate the number of Americans afflicted in 2004.
2. Using data from 2003, estimate the probability a newborn baby will be female. Locate the necessary data on the World Wide Web and submit the relevant URLs along with your answer.
1 solutions
Answer 202151 by stanbon(57203) on 2010-03-06 07:49:54 (Show Source):
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Probability-and-statistics/277713: A survey of a class of 34 students in a business school showed the following selection of majors
Accounting 10
Finance 5
Info. systems 3
Management 6
Marketing 10
Suppose you select a student. What is the probability he/she is a management major? Which concept of probability did you use to make this estimate?
1 solutions
Answer 202149 by stanbon(57203) on 2010-03-06 07:47:17 (Show Source):
You can put this solution on YOUR website!A survey of a class of 34 students in a business school showed the following selection of majors
Accounting 10
Finance 5
Info. systems 3
Management 6
Marketing 10
Suppose you select a student. What is the probability he/she is a management major? Which concept of probability did you use to make this estimate?
-------------------
Based on this empirical evidence the answer would have
to be 6/34. You have no other information so you have
to go based on what you have. There no "theoritical
answers to the question; only empirical evidence is
available.
Cheers,
Stan H.
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logarithm/277669: Solve for X. (Type an integer or simplified fraction).
log x+log (x-15)=2
1 solutions
Answer 202132 by stanbon(57203) on 2010-03-05 20:48:34 (Show Source):
You can put this solution on YOUR website!Solve for X. (Type an integer or simplified fraction).
log x+log (x-15)=2
--------------------
log(x(x-15)) = 2
x(x-15) = 10^2
x^2-15x - 100 = 0
(x-20)(x+5) = 0
Positive solution:
x = 20
--------------------
Cheers,
Stan H.
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Angles/277663: An angle measures 12 degrees less than three times its supplement. Find the measure of the angle.
1 solutions
Answer 202129 by stanbon(57203) on 2010-03-05 20:33:22 (Show Source):
You can put this solution on YOUR website!An angle measures 12 degrees less than three times its supplement. Find the measure of the angle.
-----
Equations:
x + y = 180
y = 3x-12
-----
substitute for "y" and solve for "x":
x + 3x-12 = 180
4x = 192
x = 48 degrees
y = 3x-12 = 3(48)-12 = 144-12 = 132 degrees (This is the angle you
are asked to find)
========================
Cheers,
Stan H.
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Probability-and-statistics/277664: 35% of adults say cashews are their favorite kind of nut. You randml select 12 adultseach to name his orherfavorit nut. Findthe probablility that the numberwho say cashews are their favorite nut is (a) exactly tree, (b) at least 4 and (c) at most two. IF CONVENIENT, USE TECHNOLOGY TOFINDTHE PROBABLITIES.
(A) p(3)=
(B) P(X 4)=
(C) P(X 2)=
1 solutions
Answer 202125 by stanbon(57203) on 2010-03-05 20:24:41 (Show Source):
You can put this solution on YOUR website! 35% of adults say cashews are their favorite kind of nut. You randml select 12 adultseach to name his orherfavorit nut. Findthe probablility that the numberwho say cashews are their favorite nut is (a) exactly tree, (b) at least 4 and (c) at most two. IF CONVENIENT, USE TECHNOLOGY TOFINDTHE PROBABLITIES.
---
Binomial Problem with n = 12 ; p = 0.35
Using TI-84 calculator:
(A) p(3)= binompdf(12,0.35,3) = 0.1954..
(B) P(X>=4)= 1 - binomcdf(12,0.35,3) = 0.6533
(C) P(X<=2)= binomcdf(12,0.35,2) = 0.0424
=================
Cheers,
stan H.
================
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Mixture_Word_Problems/277661: .The programmer, Sammy plans to mark up the price of his virus program 35% whereas the programmer, Martin plans to mark up the price of his virus program by 54%. If Sammy's program sells for $285 and Martin's program sells for $325, who originally had the cheaper program before the price markup?
Sammy takes 5 hours longer to complet 300 lines of code than Martin. Together Sammy and Martin can complete the code in 6 hours.
How long it takes each programmer to complete the code if they program on their own. (hint: Quadratic equaiton )and 2) at what speed they are programming lines per hour.
1 solutions
Answer 202124 by stanbon(57203) on 2010-03-05 20:20:42 (Show Source):
You can put this solution on YOUR website!The programmer, Sammy plans to mark up the price of his virus program 35% whereas the programmer, Martin plans to mark up the price of his virus program by 54%. If Sammy's program sells for $285 and Martin's program sells for $325, who originally had the cheaper program before the price markup?
---
Martin's original price:
x + 0.54x = 325; 1.54x = 325 ; x = $211.04
Sammy's original price::
x + 0.35x = 285 ; 1.35x = 285 ; x = 285/1.35 = $211.11
===========================================================
Sammy takes 5 hours longer to complet 300 lines of code than Martin. Together Sammy and Martin can complete the code in 6 hours.
How long it takes each programmer to complete the code if they program on their own. (hint: Quadratic equation)and 2) at what speed they are programming lines per hour.
---
Answered in the last hour.
================================
Cheers,
Stan H.
|
Probability-and-statistics/277633: The mean systolic blood pressure of adult males is normally
distributed with a mean of 138 (millimeters of
mercury) and a standard deviation of 9.7. What percent
of adult males have blood pressure between 161.28 and
164.9?
1 solutions
Answer 202123 by stanbon(57203) on 2010-03-05 20:10:55 (Show Source):
You can put this solution on YOUR website!The mean systolic blood pressure of adult males is normally
distributed with a mean of 138 (millimeters of
mercury) and a standard deviation of 9.7. What percent
of adult males have blood pressure between 161.28 and
164.9?
-----------------------
z(161.28) = (161.28-138)/9.7 = 2.4
---
z(164.9) = (164.9-138)/9.7 = 2.77
----------------------------------------
P(161.28< x < 164.9) = P(2.40 < z < 2.77)
Using a TI calculator I get binomcdf(2.4,2.77) = 0.0054
===========================================================
Cheers,
Stan H.
|
Inequalities/277649: solve inequality and graph the solution on the number line.
6(x-12)< 54
-
1 solutions
Answer 202122 by stanbon(57203) on 2010-03-05 20:02:38 (Show Source):
You can put this solution on YOUR website!solve inequality and graph the solution on the number line.
6(x-12)<= 54
---
x-12 <= 9
x <= 21
-----------------
Draw a number line.
Select a point and label it "21"
Put a solid circle at that point.
Draw an arrow to the left from that point.
That is the graph of the solution.
==========================================
Cheers,
Stan H.
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Quadratic_Equations/277647: WRITE (n-2)(3+(48/n))=48+22 in the standard form of a quadratic equation:
1 solutions
Answer 202121 by stanbon(57203) on 2010-03-05 19:59:03 (Show Source):
You can put this solution on YOUR website!WRITE (n-2)(3+(48/n))=48+22 in the standard form of a quadratic equation:
Let "n" be a common denominator in the 2nd factor of the 1st term.
------------------------
(n-2)[(3n+48)/n)] = 70
Multiply both sides by "n":
(n-2)(3n+48) = 70n
3n^2 + 48n - 6n - 96 = 70
3n^2 + 42n - 166 = 0
=============================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/277648: A bookstore sells 40 CDs and video in the first week, at $4 a CD and $6 a video. The total sales for that first week was $180.
Write a system of equations to represent the situation.
1 solutions
Answer 202119 by stanbon(57203) on 2010-03-05 19:53:04 (Show Source):
You can put this solution on YOUR website!A bookstore sells 40 CDs and video in the first week, at $4 a CD and $6 a video. The total sales for that first week was $180.
Write a system of equations to represent the situation.
Equation:
Quantity Equation: C + V = 40
Value Equation::: 4C + 6V= 180 dollars
----------------------------------------
Cheers,
Stan H.
|
Quadratic_Equations/277656: I have searched everywhere reading everything... I do not know how to turn this problem into a quadratic equation. Sammy takes 5 hours longer to complete 300 lines of code than Martin. Together Sammy and Martin can complete the code in 6 hours. How long does it take each programmer to complete the code if they complete on their own. At what speed is each programming lines per hour
1 solutions
Answer 202118 by stanbon(57203) on 2010-03-05 19:49:37 (Show Source):
You can put this solution on YOUR website!Sammy takes 5 hours longer to complete 300 lines of code than Martin.
Together Sammy and Martin can complete the code in 6 hours.
How long does it take each programmer to complete the code if they complete on their own.
At what speed is each programming lines per hour
-------------------------------
Let Martin time = x hr/job ; then Martin rate = 1/x job/hr
----------------------
Sammy time = (x+5)hr/job; Sammy rate = 1/(x+5) job/hr
---------------------------
Together time = 6 hr/job ; Together rate = 1/6 job/hr
---------------------------
Equation:
rate + rate = together rate
1/x + 1/(x+5) = 1/6
Multiply thru by 6x(x+5) to get:
6(x+5) + 6x = x(x+5)
12x + 30 = x^2 + 5x
x^2-7x-30 = 0
Factor:
(x-10)(x+3) = 9
Positive solution:
x = 10 hrs (Martin's time to do the job alone); his rate = 1/10 job/hr
x+5 = 15 hrs (Sammy's time to do the job alone); his rate = 1/15 job/hr
-----------------------------------
Lines per Hour?
Martin rate = (1/10)(300) = 30 lines per hour
Sammy rate = (1/15)(300) = 20 lines per hour
=================================================
Cheers,
Stan H.
|
Expressions-with-variables/277652: 8000 people attended a concert, ticket sales were $8 for adults and $4 for children. Total ticket sales was $52,000. How many adults and how many children attended. But show the work/formula.
1 solutions
Answer 202114 by stanbon(57203) on 2010-03-05 19:40:23 (Show Source):
You can put this solution on YOUR website!8000 people attended a concert, ticket sales were $8 for adults and $4 for children. Total ticket sales was $52,000. How many adults and how many children attended. But show the work/formula.
------------------
Equations:
Quantity Equation: a + c = 8000
Value Equation::: 8a + 4c=52000 dollars
-----------------------------------------
Adjust the 1st equation for elimination:
8a + 8c = 8*8000
----
Subtract the Value Equation from that and solve for "c":
4c = 64000-52000
4c = 12000
c = 3000 (# of children's tickets sold)
---
Since a + c = 8000, a = 5000 (# of adult tickets sold)
=======================================================
Cheers,
Stan H.
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