# Questions on Algebra: Expressions involving variables, substitution answered by real tutors!

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Question 994523: The family trip to Grandma's consisted of both a train ride and a car ride. The average speed of the train was 65 mph, the average speed of the car ride was 60 mph. The entire trip lasted 6 hours. Let x be the number of hours the train ride lasted. Write an expression for the total distance of the trip in miles.
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Total distance=(65mph)(x)+(60mph)(6hrs-x)
Total distance=65mph(x)+360mi-60mph(x)
Total distance=5mph(x)+360mi
.

Question 994388: I need help with the Elimination method and the problem is 4x-8y=8

Found 2 solutions by Boreal, stanbon:
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4x-8y=8
-10x+8y=28
========
Eliminate the y by adding the equations together. Notice that the -8y +8y=0, so the resulting equation will not have y. It will have been eliminated.
-6x=36
x= -6
y:--24-8y=8
-8y=-32
y= -4
=====
Check with second equation
-10(-4) + 8 (-2)
40-16=24
(-6,-4)

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need help with the Elimination method and
the problem is 4x-8y=8
and -10x+8y=28
--------
Simplify the equations:
x - 2y = 2
-5x + 4y = 14
--------
Multiply thru the top equation by 5 to get:
5x - 10y = 10
-5x + 4y = 14
----------------------
Add the equations and solve for "y"::
-6y = 24
---
y = -4
--------------------------
Solve for "x":
x - 2y = 2
x - 2*-4 = 2
x + 8 = 2
x = -6
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Cheers,
Stan H.
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Question 994190: Solve the equation.
3.7 -3.2X = 1.4X – 5.5

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3.7 -3.2X = 1.4X – 5.5 ... Add (3.2X + 5.5) to each side.
9.2 = 4.6X ... Divide each side by 4.6.
2 = X
.

Question 994170: p=√2t÷g
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Thx for letting us know.

Question 994106: A number,half of that number,and one third of that number are added.the result is 222. What is the number?
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A number, half of that number, and one third of that number are added. The result is 222. What is the number?
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x + + = 222.

Common denominator is 6. Multiply both sides by 6.

6x + 3x + 2x = 222*6,

11x = 222*6,

x = .

Calculate.

Question 994107: Ten less than double a number is the same as seven times the number. Find the number.
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Ten less than double a number is the same as seven times the number. Find the number.
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2x - 10 = 7x

5x = -10,

x = -2.

Question 994109: (x-2y)^3 for x=-1 and y=3
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.
(x-2y)^3 for x=-1 and y=3.
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= = -343.

Question 993928: A space shuttle maneuvers so that it may capture an already orbiting satellite that is 6000km.ahead.If the satellite is moving at 27,000km/h and the shuttle is moving at 29,500km/h. How long will it take the shuttle to reach the satellite? (All digits are significant)
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A space shuttle maneuvers so that it may capture an already orbiting satellite that is 6000km.ahead.If the satellite is moving at 27,000km/h and the shuttle is moving at 29,500km/h. How long will it take the shuttle to reach the satellite?
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The shuttle is "gaining on it" at 2500 km/hr
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6000/2500 = 2.4 hours

Question 993905: Solve the linear system using substitution.
4x - y = 5
4x + 4 = -4

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.
.

From the second equation you have  4x = -8,  hence,  x = -2.

Substitute it into the first equation and solve for  y.

Question 993783: Twice the sum of a number x and 6
Found 2 solutions by jim_thompson5910, rfer:
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Original StatementTranslation
the sum of a number x and 6x+6
Twice the sum of a number x and 62(x+6)

Note: 2(x+6) is equivalent to 2x+12 when you distribute the 2 through

Question 993767: A=P(1+nr) Solve for r

Question 993768: P=a+b+c solve for a

Question 993735: How do I simplify 9((x+9)/5))-5
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1 step at a time.

Question 993712: The difference between high and low tides along the Maine coast in November is 19 feet on Monday and x feet on Tuesday.write an algebraic expression to show the average number of shows Mr.Hughes attended per year if he went to the theater for 31 years
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The difference between high and low tides along the Maine coast in November is 19 feet on Monday and x feet on Tuesday.write an algebraic expression to show the average number of shows Mr.Hughes attended per year if he went to the theater for 31 years
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That's a tough one.

Question 993648: Solve by elimination method
3x-5y=-19
5x+3y=25

Found 2 solutions by Theo, Cromlix:
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3x-5y=-19
5x+3y=25

multiply the first equation by 5 and the second equation by 3.

3x - 5y = -19 becomes 15x - 25y = -95

5x + 3y = 25 becomes 15x + 9y = 75

15x - 25y = -95
15x + 9y = 75

subtract the first equation from the second equation to get:

34y = 170

divide both sides of this equation by 34 to get:

y = 5

go back to either one of your original equations and replace y with 5 and then solve for x.

3x-5y=-19
5x+3y=25

take the first equation and replace y with 5.

the equation becomes:

3x - 5*5 = -19

simplify to get:

3x - 25 = -19

add 25 to both sides of the equation to get:

3x = 6

divide both sides of the equation by 2 to get:

x = 2

go back to your second original equation of 5x+3y=25 and replace x with 2 and replace y with 5 to get:

5x + 3y = 25 becomes 5*2 + 3*5 = 25 which becomes 10 + 15 = 25 which becomes 25 = 25.

this confirms the solution is correct.

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Hi there,
3x-5y=-19.....(1)
5x+3y=25......(2)
Multiply (1) by 3 and (2) by 5
9x - 15y = -57.....(1)
25x + 15y = 125....(2)
34x.......= 68
x .......= 2
Substitute x = 2 into Equation(1)
3x - 5y = -19
3(2) - 5y = -19
6 - 5y = -19
-5y ...= -25
y......= 5
]x = 2, y = 5]
Hope this helps :-)

Question 993606: 5(2a-3b)-6(3a-4b)=

Question 993378: s/2+1=1/4s-6
what is the value of s

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.
= ,

= ,

= ,

s = -28.

Question 993198: 1) the length of a rectangle is 3in more than its width. The perimeter of the rectangle is 30in
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let the length be and the width
if the length of a rectangle is more than its width, than we have
....eq.1

if the perimeter of the rectangle is , we have
....substitute from eq.1
.......solve for

go back to ....eq.1 substitute for substitute and solve for substitute

Question 993120: R=1/r1+1/r2+1/r3 i need r2

Found 2 solutions by Alan3354, ikleyn:
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R=1/r1+1/r2+1/r3 i need r2
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1/r2 = R - (1/r1) - (1/r3)

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.

It is not sufficient info to solve the problem.

Question 993027: x + 4 and 2x - 3 = ?

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Are you looking to add the two expressions?

If that's not what you wanted, please repost and provide a clear explanation.

Question 992645: What is the answer ifa equals4 and b equals 7 and you have to evaluate the expression
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a = 4 and b = 7

ab + 4 + 3a --> (4)(7) + 4 + 3(4) = 44

Question 992621: How to simplify (xy^3/y^3)^2
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.
=     (cancel in the numerator and denominator like this)     = = .

Question 992356: Simplify expression 48x^-5g^-3/4x^-3g^6

Question 992357: Simplify expression 4(2x^3y^4)^-2

Question 992307: Hello all!,
I need clear S in next equation:
T=sqrt((R-S)/S)
How I must do?,

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T =
square both sides, this gets rid of the radical
=
multiply both sides by s
= R - S
= R
Factor out s
= R
Divide both sides by (t^2+1)
S =

Question 992227: need help on solution for this 4(1/2x+7)=12,have tried -12 on both sides but still unable to solve x-thanks
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need help on solution for this 4(1/2x+7)=12,have tried -12 on both sides but still unable to solve x-thanks
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4(1/2)x + 4*7 = 12
----
2x + 28 = 12
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2x = -16
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x = -8
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Cheers,
Stan H.

Question 992191: Hi all,
I am sorry for my question, but I don't know how solve some equations.
I need isolate "s" in this problem:
P=f/2(1+sqrt(1+4s^2/f2))

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I need isolate "s" in this problem:
P=f/2(1+sqrt(1+4s^2/f^2))
----
2 = f[1+sqrt((f^2+4s^2)/f^2)]
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2 = f[1+(1/f)sqrt(f^2+4s^2)]
====
2 = [f+sqrt(f^2+4s^2)]
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2-f = sqrt(f^2+4s^2)
----
4-4f+f^2 = f^2 + 4s^2
----
4s^2 = 4-4f
-----
s^2 = 1 - f
-----
s = sqrt(1-f)
------------------
Cheers,
Stan H.
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Question 992090: x=25a/9b solve for b

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Multiply both sides by

John

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

Question 991983: Hello,
I have next problem:
T=2Pi sqrt(K^2+h^2/gh)
and I have to isolate the variable K, some help please?
rookie78

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T=2Pi sqrt(K^2+h^2/gh)
and I have to isolate the variable K
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Question 991567: 4(4-w)=3(2w+2)

Question 991520: A student was asked to use the formula for the perimeter of a rectangle, P=2L+2w, to solve for L. The student came up with a n answer, P-2w=2L. What error did the student make? Explain. Then solve for L.
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Student did not finish. He stopped at finding 2L, but he was assigned to solve for L. Missing step is multiplication property of equality, using the multiplicative inverse of 2.

Question 991513: The formula c=5p+215 relates c, the total cost in dollars of hosting a birthday party at a skating rink, to p, the number of people attending. If Allie's parents are willing to spend $300 for a party, how many people can attend? Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! Replace the variable c with 300 and solve for p. John My calculator said it, I believe it, that settles it Question 991497: Please help.. Represent (or model) each situation with an algebraic equation. The quotient of p divided by r, decreased by the product of p and r, is 5. Answer by MathLover1(11324) (Show Source): You can put this solution on YOUR website! The quotient of divided by : decreased: minus the product of and : is : equal to put all together: Question 991270: the perimeter of an equilateral triangle, whose side is x units, is thirty. Answer by solver91311(20879) (Show Source): You can put this solution on YOUR website! So what is your question? Do you not understand what "perimeter" or "equilateral" means? What part of this question is giving you difficulty? What have you tried so far? John My calculator said it, I believe it, that settles it Question 991235: In algebraic expression twice the difference between c and four Answer by stanbon(69061) (Show Source): You can put this solution on YOUR website! In algebraic expression twice the difference between c and four ---------- Ans: 2(c-4) -------------- cheers, Stan H. ---------- Question 991153: you sold a used video game to a friend of yours for$18.00 less than the original cost.if you sold the video game to your friend for \$35.00, what was the original cost of the game?
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Question 991034: The factory produces b bicycle an hour and runs for h hours a day. Write a variable expression for the number of bicycle tires the factory uses each day. Evaluate the expression when b =50 and h =16
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[ bicycles / hr ] x [ h hrs / day ] = [ bicycles / day ]
and
[ bicycles / day ] x [ tires / bicycle ] = [ tires / day ]
bicycles / day =
tires / day =
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Question 990822: The sum of m and quotient of n divided by 2 .
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The sum of m and quotient of n divided by 2
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m +

Question 990760: 9×^2 y^3/12xy^4

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What about it? Are we supposed to guess what you want?

John

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

Question 990589: Write an algebraic expression for the verbal description.
The perimeter of a rectangle with a width x and a length that is twice the width.

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if width w=x----(1)
and lenght L=2x----(2)
Then
perimeter(P)=2(L+w)---(3)
put equ 1 and 2 in 3
Therefore,
p=2(x+2x)
p=2(3x)
p=6x
HOPE THIS HELPS?
;;Timnewman::

Question 990511: 7 times a number increased by 10 is equal to 8 less than 4 times the number. Determine the number?