Questions on Word Problems: Translating English into Algebreze answered by real tutors!

You can put this solution on YOUR website!
You left something out. Train B would have to leave some time after Train A for this to make sense.
:
Train leaves a station traveling at 64 kilometers per hour. Train B leaves the
the station 4 hrs later going the same direction at 74 kilometers per hour.
How long does it take train b to catch up to train a?
:
Let t = travel time required by B to catch up with A
then
(t+4) = travel time of A, when it's overtaken by B
:
When this happens both trains will have traveled the same distance
Write a distance equation from fact (Dist = speed * time)
:
B dist = A dist
74t = 64(t+4)
:
74t = 64t + 256
:
74t - 64t = 256
:
10t = 256
t =
t = 25.6 hrs is the travel time of Train B to catch up with A
:
:
Check solution by ensuring they both went the same dist(Train A time = 29.6 hrs)
74 * 25.6 = 1894.4 mi
64 * 29.6 = 1894.4 mi

You can put this solution on YOUR website!
lets call one travelers rate r and the other r+20. time is the same and lets call the distances x and 125-x
r(5/4)=x.........eq 1
(r+20)(5/4)=125-x..eq 2
lets use x's value from 1st equation and plug it into the 2nd eq
r+20(5/4)=125-(5/4)r
multiply both sides by 4
5r+100=500-5r
10r=400
speed of the slower traveler
speed of the faster traveler

You can put this solution on YOUR website!
.06X+.05(1,000-X)=58
.06X+50-.05X=58
.01X=58-50
.01X=8
X=8/.01
X=$800 INVESTED @ 6%
1,000-800=$200 INVESTED @5%
PROOF:
.06*800+.05*200=58
48+10=58
58=58

You can put this solution on YOUR website!
The smaller of two numbers is 3 less that the larger. Twice the larger plus 4 times the smaller is 36. Find the numbers
solution:
Let the two numbers be x and y.
Let the smaller of the two be x
x= y-3
2y+4x = 36
Hence we haev to solve the following linear syste of equation
x-y = -3
4x+2y = 36=> 2x+y = 9
adding the two equations,
3x = 6=> x= 2
y = 5
The numbers are 2 and 5.

You can put this solution on YOUR website!
Let the two numbers be x and y
Let x be the greater number and y be the smaller number
x = y+5
y+2x = 22
so u have to solve this system of linear equations
x-y = 5
2x + y = 22
adding,
3x = 27
x = 9
y =4
the numbers are 9 and 4

You can put this solution on YOUR website!
Let = mystery number
Condition:


----->
, The Mystery Number
Check,



Thank you,
Jojo

You can put this solution on YOUR website!

1st length of cut = inches
2nd length of cut = inches
Therefore with total length of 32inches:

----->
, 1st length of cut
, 2nd length of cut
Check:

Thank you,
Jojo

You can put this solution on YOUR website!

Let =the number
1st condition: eleven less the quotient of number & 3:
2nd condition: equals to 18:
continuing,
, combine similar terms
, perform operations, then cross multiply


Check via 2nd condition:


, good!
Thank you,
Jojo

You can put this solution on YOUR website!
You are working with three different numbers.
When the first number is added to twice the other two numbers, the result is 64
x + 2y + 2z = 64
;
When the second number is added to twice the other two numbers the result is 62.
2x + y + 2z = 62
:
Finally, when the third number is added to twice the other two numbers, the
result is 59.
2x + 2y + z = 59
:
Using the 1st two equations
x + 2y + 2z = 64
2x + y + 2z = 62
-------------------subtraction eliminates z
-x + y = 2
y = x+2
:
Multiply the 3rd equation by 2, and subtract the 1st equation
4x + 4y + 2z = 118
x + 2y + 2z = 64
-------------------subtraction eliminates z again
3x + 2y = 54
Substitute(x+2) for y
3x + 2(x+2) = 54
3x + 2x + 4 = 54
5x = 54 - 4
5x = 50
x = 10 is the 1st number
then
y = 10+2
y = 12 is the 2nd number
:
Find z using the 3rd equation
2(10) + 2(12) + z = 59
20 + 24 + z = 59
z = 59 - 44
z = 15 is the 3rd number
:
:
Check solution in the 2nd equation
2(10) + 12 + 2(15) = 62
:
what are the three numbers?? 10, 12, 15
:

You can put this solution on YOUR website!
Three lighthouses on three nearby islands flash their lights every evening
beginning at 8:35pm. On one island, the ligh flashes every 45 seconds.
The lighthouse on the second island has a light that flashes every 2 minutes.
The third lighthouse flashes a light every 1 1/4 minutes.
At what time will all three lights flash together again?
:
Convert 2 min to seconds and 1.25 min to seconds.
:
So we have:
:
Lt1 = 45; Lt2 = 120; Lt3 = 75
:
Prime factor each:
45: 3,3,5,
120: 2,2,2,3,5
75: 3,5,5
:
Lcm of all three: 2,2,2,3,3,5,5 Multiply this: 1800 secs they will all Flash
:
1800/60 = 30 min: At 9:05Pm this should occur

You can put this solution on YOUR website!
you are looking for the lowest common multiple

45sec = 3 * 15

2min = 120sec = 8 * 15

1 1/4 min = 75sec = 5 * 15

LCM = 15 * 3 * 8 * 5 = 1800sec = 30min

so, every half hour they flash together

You can put this solution on YOUR website!
FACTORING EACH OPF THE TIMES IN MINUTES WE THEN FIND THE LOWEST COMMON DENOMINATOR.
45=2*2*2*5
120=2*2*2*3*5
75=3*5*5
NOW WE HAVE 2*2*2*3*5*5=600 MINUTES AFTER 8:35 THEY WILL ALL FLASH.
600MIN.=10 HOURS.
THUS THE TIME WILL BE 8:35 PM+10:00=6:35 AM.

You can put this solution on YOUR website!
The highway has a 6% grade on descent, which means it's slope is - 6/100. Driving on this road, you notice from elevation signs that you have descended a distance of 1000 ft. What is the change in your horizontal distance?
------------------
slope = vertical change/horizontal change
----------------------------
Use a proportion:
1000/x = 6/100
x = 100000/6 = 16,666.67 ft (horizontal distance)
=====================================================
Cheers,
Stan H.

You can put this solution on YOUR website!
a group rental a cabin for 300$ for weekend if one more person goes alonge the price per person is reduces by 10$ how many people are in the original group
=================
Let the original number in the group be "x".
The average cost is (total cost)/(number of persons)
Average cost per person is 300/x dollars.
--------------------------
If one more person joins the average cost will be 300/(x+1) dollars.
-------------------------
EQUATION:
original cost - new cost = 10 dollars
300/x - 300/(x+1) = 1o
300x + 300 - 300x = 10x(x+1)
x(x+1) = 30
x^2+x-30 = 0
(x+6)(x-5)=0
x = 5 (original size of the group was 5)
=========================
Cheers,
Stan H.

You can put this solution on YOUR website!
This question is not complete.
Find the rate of what??????

You can put this solution on YOUR website!
One number is four more than a second number. Two times the first number is 12 more than four times the second number.
.
Let x = second number
then from "One number is four more than a second number"
x+4 = first number
.
From "Two times the first number is 12 more than four times the second number" we get our equation:
2(x+4) = 12 + 4x
2x+8 = 12 + 4x
8 = 12 + 2x
-4 = 2x
-2 = x (second number)
.
First number:
x+4 = -2+4 = 2 (first number)

You can put this solution on YOUR website!
.25x+.05(2x)=4.90
.25x+.10x=4.90
.35x=4.90
x=4.90/.35
x=14 quarters.
2*14=28 nickles.
Proof:
.25*14+.05*28=4.90
3.50+1.40=4.90
4.90=4.90

You can put this solution on YOUR website!
8(x+x+4.50)=372
8(2x+4.50)=372
16x+36=372
16x=372-36
16x=336
x=336/16
x=$21 per hour for the apprentice.
21+4.50=$25.50 for the plumber.
Proof:
8(21+25.50)=372
8*46.50=372
372=372

You can put this solution on YOUR website!
Mickey mows lawns 5 days a week in the summer and he works the same number of hours each day. If he works a total of 20 hours, write an equation to represent how many hours he works each day. Solve and check your equation.
total days of work = 5
total hours of work = 20
Let x = hours he works each day
Let h = total hours
Let d = total days
We now have this equation:
x = h/d
x = (total hours)/(total days)
x = 20 hours/5 days
x = 4 hours
THE PROVE:
Let x = 4, h = 20 and d = 5 in our equation.
If we get the same answer on both sides of the equation, then we will know if Mickey works 4 hours each day or not.

x = h/d
4 = 20/5
4 = 4...It check!!
So, our final answer is 4 hours each day.

You can put this solution on YOUR website!
The Perimeter P = 2(length(L)) + 2(width(W)) Now we are given that L = 3W-6 and that the perimeter =76ft so plugging in known values we have 76 = 2(3W-6)+ 2W solving for the width W... 76 = 6W-12+2W simplifying further by adding 12 to each side and combining like terms we arrive at 88 = 8W. divide each side by 8 and you conclude that W=11 Now since L=3W-6 we have 3(11)-6 which equals 27
Answer W=11
L=27

You can put this solution on YOUR website!
A rectangular field has a width of w meters. The length of the field is 2 meters less than 5 times the width. Write an expression that represents the area of the rectangle.
Width = w
Length = 5w - 2
Area of rectangle is: Area = length times width
The expression that represents your area for this rectangle is:
A = (5w - 2)(w)
Did you follow?

You can put this solution on YOUR website!
total messages for the month is 3850 as follows:
-----
let C = cost
let M = number of messages greater than 1000
formula is:
C = $10 + $.01*M
-----
substitute known values in equation.
$38.50 = $10 + $.01*M
subtract $10 from both sides of equation.
$28.5 = $.01*M
divide both sides of the equation by $.01.
2850 = M
-----
looks like number of messages greater than 1000 is 2850.
to prove, substitute in original equation.
-----
$38.50 = $10.00 + $.01*2850
$38.50 = $10.00 + $28.50
$38.50 = $38.50
-----
the value of 2850 for M is good.
total messages for the month would be 2850 + 1000 = 3850.
-----

You can put this solution on YOUR website!
You have the formula in your head
You just can't get it out
Let = Miriam's monthly bill
Let = the number of text messages sent in the
month of June by Miriam
= the number of text messages over
Miriam's monthly bill is:
dollars
Her monthly bill is $38.50. I'll show it in terms of cents
cents
Subtract from both sides


Add to both sides

messages
----------------------------
It might help to go over the units involved in the 1st
formula which was
dollars
The really stands for ($10/1000 messages)x(1000 messages)
And the other term is really (.1 dollars/message)x(t - 1000 messages)
The units work out to dollars for both terms
----------------------------
You can check the answer





OK

You can put this solution on YOUR website!
A rental company charges $65 a day and 30 cents a mile for renting a truck. Michael rents a truck for 3 days, and his bill comes to $275. How many miles did he drive?
I can figure out that the answer is 400 miles, but I don't know how to put it in an algebraic equation form.

400 miles cannot be correct, for 30 cents times 
400 miles gives $120. And $65 times 3 days gives $195. 

But adding $195 + $120 gives $315, not $275.

----------------------

Just think how the total bill was figured.  It was this way:

1.  $65 TIMES THE NUMBER OF DAYS 

PLUS 

2.  $0.30 TIMES THE NUMBER OF MILES

EQUALS

3.  THE TOTAL BILL 

---------------------

Let's look at 1.  That's $65 times 3 days or $195.

Let's look at 2.  We don't know the number of miles, so we let
the letter x represent this unknown number.  But we can
multiply $.30 by x anyway and get $.30x

Let's look at 3.  That's given as $275.

So we have

$195 PLUS $.30x EQUALS $275

or dropping the dollar signs, and using + for PLUS and = 
for EQUALS:

195 + .30x = 275

Now we subtract 195 from both sides:

      .30x = 80

Now we divide both sides by .30



       

So it's not 400 miles, it's 266.67 miles.

Edwin

You can put this solution on YOUR website!
let C = cost to rent
let D = number of days
let M = number of miles.
-----
formula is:
C = ($65.00 * D) + ($.3 * M)
-----
in your problem,
C = $275.00
D = 3
-----
substitute known values in equation.
$275.00 = $65.00 * 3 + $.3 * M
perform indicated operations.
$275.00 = $195.00 + $.3 * M
subtract 195 from both sides of equation.
$275.00 - $195.00 = $.3 * M
perform indicated operations.
$80.00 = $.3 * M
divide both sides of equation by $.3
$80.00 / $.3 = M
perform indicated operations.
266.6666666667 = M
which is the same as
266 + 2/3 = M (.666666667 is same as 2/3)
-----
answer is 266 and 2/3 miles.
not sure how you got 400 but it isn't right.
-----
plugging values into original equation will help you to see this.
-----
C = 3*65 + .3*(400) = 195 + 120 = 315 (not equal to 275)
C = 3*65 + .3 (266 + 2/3) = 195 + 79.8 + .2 = 195 + 80 = 275
-----

You can put this solution on YOUR website!
annual salary = 12 * monthly salary plus bonus.
your equation is:
97300 = 12*x + 8500
subtract 8500 from both sides gets
88800 = 12*x
divide both sides of 12 gets
7400 = x
which is same as
x = 7400.
-----
good thinking.

You can put this solution on YOUR website!
Let the numbers be: x, (x+1)
:
Just write an equation for what it says:
:
"The sum of two consecutive numbers is 45."
x + (x+1) = 45
2x + 1 = 45
2x = 45 - 1
2x = 44
x =
x = 22 & 23 are the numbers
:
Assume this is another problem
:
Using x, x+1 again:
"If 4 times the smaller number is increased by 3 times the larger number, the result is 150."
4x + 3(x+1) = 150
4x + 3x + 3 = 150
7x = 150 - 3
7x = 147
x = 21, and 22 are the numbers

You can put this solution on YOUR website!
3+3=6 answer.

You can put this solution on YOUR website!
when Min overtakes Lew, they have travelled the same distance __ d=rt

Min drives 28mph for 2h

Lew rides Xmph for (5+2)h

28 * 2 = X * 7 __ 56=7X __ 8=X

You can put this solution on YOUR website!
solve by substitution or elimination method: 3x-2y=8
-12x+8y=32
The first thing to do is to isolate one of the letters.
It is YOUR CHOICE which letter to isolate first.
To isolate means to place the letter of choice ALL ALONE on one side of the equation.
I will isolate y in the equation 3x - 2y = 8.
Subtracting 3x from both sides we get this:
-2y = -3x + 8
The letter y is not alone. See it? It has a friend named coefficient -2.
To get y alone, we now divide both sides by -2.
y = (-3x + 8)/-2
y = (3x/2) - 4
Since we now found y to be (3x/2) - 4, we plug that into -12x + 8y = 32 to find the value of x.
LOOK:
-12x + 8(3x/2) - 4) = 32
-12x + 12x - 32 = 32....STOP!!!!!
If you look carefully, on the left side of the equation you will see that -12x and 12x BOTH CANCEL OUT.
What does this mean?
Since x is gone from the system of equations, then we can STOP RIGHT HERE and say that this particular system of equations in two variables has NO SOLUTION.
This is your final answer: NO SOLUTION.
Did you follow?

You can put this solution on YOUR website!
4x

You can put this solution on YOUR website!

Let "x"="what you have"
So, if you have 2 much more ----->
will give you 4 -------> , working eqn
continuing,
, transpose

, Answer (original what you have)
Go back working eqn,
, oks
Thank you,
Jojo

You can put this solution on YOUR website!

Complete the squares in both x and y.
Take 1/2 of both the x and y coefficient and square it.
Add that number to both sides of the equation.




Compare this equation to a general form of a circle centered at (h,k) with a radius, R.

.
.
.
This is an equation of a circle centered at (-4,-3) with a radius of 7.

You can put this solution on YOUR website!
he revenue, R, of an electronics manufacturer for selling x handheld organizers is given by R=0.25x^2-100x. The revenue of a competing manufacturers for selling similar products is R=75x. Under what circumstances will both manufacturers have the same revenue?
:
Just make the two expression equal to each other and find x
0.25x^2-100x = 75x
:
.25x^2 - 100x - 75x = 0
:
.25x^2 - 175x = 0
;
Get rid of the decimal, multiply equation by 4
x^2 - 700x = 0
:
Factor out x
x(x - 700) = 0
:
Two solutions:
x = 0 (when they both sell nothing, of course they will be equal)
and
x = 700 units sold they will be equal, probably the solution they want
:
:
Check for equal revenue
75(700) = $52,500
:
.25(700^2) - 100(700) =
122500 - 70000 = $52,500

You can put this solution on YOUR website!
(25-2x)(40-2x)=700
1,000-130x+4x^2=700
4x^2-130x+1,000-700=0
4x^2-130x+300=0
(2x-60)(2x-5)=0
2x-5=0
2x=5
x=5/2
x=2.5 in. is the sqare that is cut.
Proof:
(25-2*2.5)(40-2*2.5)=700
(25-5)(40-5)=700
20*35=700
700=700

You can put this solution on YOUR website!
in 1999 he sold 50
in 2004 he sold 180
change in number of cars sold is 180 - 50 = 130.
change in number of years is 2004 - 1999 = 5
change in number of cars sold per year is 130 / 5 = 26

You can put this solution on YOUR website!
formula is t = $28.95 * d + .15 * m
where d is number of days and m is number of miles and t is total cost.
then you just substitute the values.
you rented for 1 day and drove 220 miles.
formula becomes t = ($28.95 * 1) + (.15 * 220)
this becomes t = $28.95 + $33.00 which equals $61.95.
so t = $61.95
-----

You can put this solution on YOUR website!
Charge=Days+Miles

Where D is the number of days, M is the number of miles.
.
.
.
For D=1 day and M=220 miles,




.
.
.
The charge would be $61.95.

You can put this solution on YOUR website!
x, x+2, x+4 are the 3 integers.
5(x+2)=2(x+x+4)
5x+10=2(2x+4)
5x+10=4x+8
5x-4x=8-10
x=-2 the first integer.
-2+2=0 for the second integer.
-2+4=2 for the largest integer.
Proof:
5(0)=2(-2+2)
0=2*0
0=0

You can put this solution on YOUR website!
find three consecutive even integters such that five times the second equals twice the sum of the first and third
Let the three integers be: x, x+2, x+4
then 5(x+2) = 2[x+(x+4)]
solve it: 5x + 10 = 2(2x + 4)
simplify 5x + 10 = 4x + 8
5x -4x = 8 - 10
x = -2
so the three integers are -2, 0, 2

You can put this solution on YOUR website!
270,000+38X<90X
38X-90X<-270,000
-52X<-270,000
X>-270,000/-52 DIVIDING BY A NEGATIVE VALUE CHANGES THE < SIGN TO A > SIGN.
X>5,192.3 IS THE NUMER OF THAT MUST BE SOLD.
PROOF:
LET X=5,193
270,000+38*5,193<90*5,193
270,000+197,334<467,370
467,334<467,370

You can put this solution on YOUR website!
Write the concentration equation.





.
.
.
15 gallons of distilled water will bring it to 25% solution.

You can put this solution on YOUR website!
A gardener has a garden that is 20 feet wide and 100 feet long. She wants to
have a stone border (along all 4 edges of the garden and inside of the garden)
of uniform width. The stone border should use 100 square feet of crushed stone.
How wide should the border be in inches?
:
Let x = the width of the stone border
:
Find the area of the whole garden area:
20 * 100 = 2000 sq/ft
:
Find the area of the garden inside the stone border
(20-2x) * (100-2x) = 2000 - 240x + 4x^2 sq/ft
:
total area - inside stone border area = border area (100 sq/ft)
2000 - (2000 - 240x + 4x^2) = 100
:
removing brackets changes the signs
2000 - 2000 + 240x - 4x^2 - 100 = 0
:
-4x^2 + 240x - 100 = 0
:
Simplify equation, divide by -4, see if it will factor,
x^2 - 60x + 25 = 0:
No, so use the quadratic formula to solve this:

In this problem a=1; b=-60; c=25



Only one solution will make sense:

x =
x = .42 ft width of the stone border; about (.42 * 12 = 5 inches)
:
;
Check solution; find the area inside the border, subtract from 2000 sq/ft
(20-.84)*(100-.84) = 1899.9 ~ 1900 sq/ft
2000 - 1900 = 100 sq/ft as given

You can put this solution on YOUR website!
Hann paid $1.50 each for programs to the game, he sold all but 20 of them for $3 dollars each and made a profit of $15. how many programs did he buy?
:
Let x = number he bought
then
(x-20) = number he sold
:
Cost = 1.50x
Revenue = 3(x-20)
:
Revenue - cost = profit ($15)
3(x-20) - 1.5x = 15
:
3x - 60 - 1.5x = 15
:
3x - 1.5x = 15 + 60
:
1.5x = 75
x =
x = 50 programs he bought
:
:
Check our solutions (no. sold: 50-20=30)
3(30) - 1.5(50) =
90 - 75 = 15

You can put this solution on YOUR website!
A homeowner wants to fence a rectangular garden using 120ft of fencing. The side of the garage will be used as one side of the rectangle. Find the dimensions for which the area is a maximum.
:
The perimeter equation with one side being the garage:
L + 2W = 120
or
L = (120 - 2W)
;
Area = W * L
Substitute (120-2W) for L and you have:
A = W(120-2W)
A = 120W - 2W^2
This can be arranged as a quadratic equation
-2W^2 + 120W = 0
:
To find the maximum, find the axis symmetry using x =
In this equation:
W =
W =
W = +30 ft is the width for max area
Find L
L = 120 - 2(30)
L = 60 ft is the length
;
Find the max area, substitute 30 for W in the equation
A = -2(30^2) + 120(30)
A = -1800 = 3600
A = +1800 sq/ft is the maximum area
:
:
Check solution by finding the area with the dimensions:
60 * 30 = 1800 sq/ft