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

You can put this solution on YOUR website!
emily and Camille started from the same city and drove in opposite directions on the freeway. After 3 hours they were 354 miles apart.
Let e be Emily's rate; let c be Camille's rate
----
distance + distance = 354 miles
3e + 3c = 354
e + c = 118
-----------------------
If they had gone in the same direction, Emily would have been 18 miles ahead of Camille. How fast did each woman drive?
3e - 3c = 18
e - c = 6
=======================
Two equations:
e + c = 118
e - c = 6
-------------
Add and solve for "e":
2e = 124
e = 62 mph (Emily's rate)
------
Solve for "c":
e + c = 118
62 + c = 118
c = 56 mph (Camille"s rate)
=============================
Cheers,
Stan H.
===========

You can put this solution on YOUR website!


Since they were traveling in opposite directions, they were moving apart at the sum of their speeds. Since they were 354 miles apart in 3 hours, the sum of their speeds must be 116 mph. Had they been going in the same direction, their distance apart would have been a function of the difference in their speeds. 18 miles in 3 hours is 6 mph difference.





Solve the 2X2 system.

John

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

You can put this solution on YOUR website!
Investment Part I 12.00% per annum ----x
Investment part II 14.00% per annum ----y
The sum of the investments is $35,000.00
The sum of individual interests = $4,460.00
x + y 35000 ------------------------1
12.00% x + 14.00% y = $4,460.00
Multiply by 100
12 x + 14 y = $446,000.00--------2

Multiply (1) by -12
we get

-12 x -12 y = -420000.00

Add this to (2)

0 x 2 y = $26,000.00

divide by 2

y = $13,000.00 investment at
Balance $22,000.00 investment at
CHECK
$22,000.00 @ 12.00% $2,640.00
$13,000.00 @ 14.00% $1,820.00
Total -------------------- $4,460.00

You can put this solution on YOUR website!
A pot contains 4 L of brine at a concentration of 80 g/L. How much of the water should be boiled off to increase the concentration to 200 g/L?
**
let x=liters of water to be boiled off
80*4=200(4-x)
320=800-200x
200x=480
x=2.4 L (ans)

You can put this solution on YOUR website!
(1/2)*8=4 cats.

You can put this solution on YOUR website!
Let 'b' be the price of a bagel and 'c' the price of a cup of coffee. Then we have 3c+2b=12.75 and 2c+5b=14. If we solve, we get c=$3.25, b=$1.50. That's expensive coffee!

You can put this solution on YOUR website!
boat rate in still water = 5mph
upstream rate = 5-x
downstream rate = 5+x
time upstream = 1/4 hour
time downstream = 1/6 hour
Distance up and down is the same
d=rt
(5-x)*1/4 = (5+x)*1/6
multiply the equation by 12
3(5-x)=2(5+x)
15-3x=10+2x
5x=5
x=1 mph speed of current
D= (5-1)*1/4 = 1 mile

You can put this solution on YOUR website!
It costs $395 to get the tools/equipment you need just to start, before you manufacture anything.
After that, it costs $7.50 to make each kit, so making x kits costs $7.5 times x, on top of your original $395 investment.
The cost to produce seal kits (in $) is
, and that's your answer.
Going a little further:
It will take making and selling a few kits to break even. If you sell x of them at $22.95 each, you would get $22.95 times x in sales. In $, that is .
To break even, that should equal the cost of making x kits, so

Solving that equation
--> --> --> --> --> x=about 25.6
If you make and sell 25 kits you will have a tiny loss.
If you make and sell 26 kits you will have a tiny profit.
Looking at it graphically, your cost and sales as a function of number of kits produced and sold can be plotted like this
C(x) in red, S(x) in green

You can put this solution on YOUR website!
8/4=x/2

8*2 = 4x

16 = 4x

16/4 = x

x = 4


So the lawn ornament is 4 ft tall.
-------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

You can put this solution on YOUR website!
Find the present value that will give a future value of $9,280 at 9.75 % compounded monthly for 2 years and 3 months.

A = P(1 + )nt

where 

A stands for the finAl amount
P stands for the the Previous Principle, The Peginning amount :)
r stands for the rate expressed as a decimal.
n represents the number of times per year the interest is compounded.
t represents the time in years.

A = 9280
P = ?
r = .0975
n = 12  
t =  = 2.25

A = P(1 + )nt
9280 = P(1 + )12·2.25

9280 = P(1 + .0079166667)27
9280 = P(1.007916667)27
9280 = P(1.237271244)

Divide both sides by 1.237271244

 = 7500.376369

Answer: $7500.38

Edwin

You can put this solution on YOUR website!
A van travels for two hours at an average speed of 40 miles per hour.
1st distance = 80 miles.
-----------------------------------
For how long must the van then travel at an average speed of 55 miles per hour to raise the overall average speed to 45 miles per hour?
Let that time = x hrs;
Then distance traveled is 55x
-----------------------------------
What is the total time traveled?
Final average = (total distance)/(total time) = (80+55x)/(2 + x)
-----
Equation:
45 = (80+55x)/(2+x)
90 + 45x = 80 + 55x
10x = 10
x = 1 hr. (time the van traveled at 55 mph)
=============================================
Cheers,
Stan H.
==============

You can put this solution on YOUR website!
One number is 11 more than 3 times another number.
Their sum is 55. Find the SMALLER
---
smaller: x
larger: 3x+11
---
Equation:
x + 3x+11 = 55
4x = 44
x = 11 (smaller)
========================
Cheers,
Stan H.
========================

You can put this solution on YOUR website!
This is a strangely worded strange problem.
The strangest aspect of the problem is that the solution, as calculated, would not be a whole number, but that is the way this kind of prediction works. You have to take it about as seriously as the weather forecast. They may calculate that 1234.127 jobs will probably be lost in a certain occupation, and will report it as 1234.
The way I read it, the problem means to say the following:
The number of lost telephone operator jobs is expected to be twice the number of lost fisherman jobs plus 8000.
The number of lost sewing machine operator jobs is expected to be ten times the number of lost telephone operator jobs minus 1000.
Once we agree on what the problem meant, we can get to work to solve it. We can disagree on how to do that too, so I am providing two ways. You can figure out what solution your teacher expected.
THE GUESS AND CHECK WAY TO SOLVE IT (for elementary grades & others)
There are obviously less fishermen and less jobs were lost in that occupation.
{For my guess and checks, I make a table with a first column for the number of lost fisherman jobs and columns for the numbers of jobs lost in the other two occupations and a for the total of the 3 occupations. I write a guess for the first column, and calculate the corresponding numbers for the other columns. Each new guess fills one more line in the table. I cannot make a good table on this website, but I am including the explanations for all calculations and guessing decisions. The entire explanation below may look long and complicated, but the calculation work is not that complicated).
IF 1000 fisherman jobs were lost, the number of lost telephone operator jobs would be , and the number of lost sewing machine operator jobs would be . Then the total number of jobs lost among the three occupations would be 1,000+10,000+99,000=110,000.
Obviously the situation was worse than that. Let's try the next guess.
IF 2000 fisherman jobs were lost, the number of lost telephone operator jobs would be , and the number of lost sewing machine operator jobs would be . Then the total number of jobs lost among the three occupations would be 2,000+12,000+119,000=133,000.
Obviously the situation was worse than that, but we are getting close to the answer. Let's try the next guess.
IF 2200 fisherman jobs were lost, the number of lost telephone operator jobs would be , and the number of lost sewing machine operator jobs would be . Then the total number of jobs lost among the three occupations would be 2,200+12,400+123,000=137,600.
So the number of lost fisherman jobs must be between 2000 and 2200, closer to 2200. Let's try the next guess.
IF 2150 fisherman jobs were lost, the number of lost telephone operator jobs would be , and the number of lost sewing machine operator jobs would be . Then the total number of jobs lost among the three occupations would be 2,150+12,300+122,000=136,450.
So the number of lost fisherman jobs must be between 2150 and 2200. Let's try the next guess.
IF 2175 fisherman jobs were lost, the number of lost telephone operator jobs would be , and the number of lost sewing machine operator jobs would be . Then the total number of jobs lost among the three occupations would be 2,175+12,350+122,500=137,025.
So the number of lost fisherman jobs may be a little less than 2,175, but we are very, very close. Let's try the next guess.
IF 2173 fisherman jobs were lost, the number of lost telephone operator jobs would be , and the number of lost sewing machine operator jobs would be . Then the total number of jobs lost among the three occupations would be 2,173+12,346+122,460=136,979.
IF 2174 fisherman jobs were lost, the number of lost telephone operator jobs would be , and the number of lost sewing machine operator jobs would be . Then the total number of jobs lost among the three occupations would be 2,174+12,348+122,480=137,002.
So, 2173 lost fisherman jobs was too few, and 2174 was too many, but closer. That last try is as close as we will get, and that will be our solution, because we are not allowed to split fishermen.
USING A SYSTEM OF LINEAR EQUATIONS (for those studying systems of equations)
We can set up a system of linear equations
Let f be the number of lost fisherman jobs.
Let f be the number of lost fisherman jobs.
Let f be the number of lost fisherman jobs.
We write our equations:



Strangely enough, this system begs for substitution.
Substituting into we get
--> -->
Substituting and into we get
--> --> -->
We cannot split fishermen. Since , we take f=2174 as our approximation.
The rest is
--> -->
--> -->

You can put this solution on YOUR website!
When a bucket is filled 3/8 of its capacity its weight is 10 kg.
If it is filled 3/5 of its capacity its weight is 14.5 kg.
How much will its weight be when it is filled to the full capacity?
:
We can convert these fractions to exact decimals
= .375
= .6
:
Assign the values as follows
x1 = .375; y1 = 10
x2 = .600; y2 = 14.5
:
Find the slope m =
m = = = 20
:
Use the point/slope form to construct an equation: y - y1 = m(x - x1)
y - 10 = 20(x - .375)
y - 10 = 20x - 7.5
y = 20x - 7.5 + 10
y = 20x + 2.5, is the equation
:
Bucket is full when x = 1
y = 20(1) + 2.5
y = 22.5 kg for a full bucket